Construct a Venn diagram to illustrate this information: 30 students study one or more of three languages: French, German and Mandarin 5 study all three languages. 6 study Mandarin only. 2 study French and Mandarin but not German 15 students in total study Mandarin 2 study only French 3 study only German.

We need to construct a Venn Diagram based on the given information It is given that 30 students study one or more of three languages: French, German and Mandarin. Let us draw a rectangle representing the universal set of all languages. And, let us draw three circles representing the languages French F , German G and Mandarin M . It is given that 5 study all three languages, so we have Further, it is given that 6 study only Mandarin, 2 study French and Mandarin but not German, So, we have It is given that 15 students in total study Mandarin So, the number of students studying Mandarin and German = 15 - 5 + 2 + 6 = 15 - 13 = 2 Now, it is given that 2 study only french and 3 study only German. So, we have Now, it is given that total 30 students study these three languages. So, the number of students studying French and German = 30 - 5 + 2 + 2 + 6 + 2 + 3 = 30 - 20 = 10 Hence, the Venn Diagram representation of the given information is as follows:

Construct a Venn diagram to illustrate this information: 30 students study one or more of three languages: French, German and Mandarin 5 study all three languages. 6 study Mandarin only. 2 study French and Mandarin but not German 15 students in total study Mandarin 2 study only French 3 study only German. From your diagram, find n F r e n c h and n U . Use these to find the probability that a student picked at random studies French.

We need to construct a Venn Diagram based on the given information It is given that 30 students study one or more of three languages: French, German and Mandarin. Let us draw a rectangle representing the universal set of all languages. And, let us draw three circles representing the languages French F , German G and Mandarin M . It is given that 5 study all three languages, so we have Further, it is given that 6 study only Mandarin, 2 study French and Mandarin but not German, So, we have It is given that 15 students in total study Mandarin So, the number of students studying Mandarin and German = 15 - 5 + 2 + 6 = 15 - 13 = 2 Now, it is given that 2 study only french and 3 study only German. So, we have Now, it is given that total 30 students study these three languages. So, the number of students studying French and German = 30 - 5 + 2 + 2 + 6 + 2 + 3 = 30 - 20 = 10 Hence, the Venn Diagram representation of the given information is as follows: Thus, we have n F = 2 + 2 + 5 + 10 = 19 Total number of students in the universal set = 30 Thus, the probability that student picked up studies French = Number of students who study French Total number of students in the universal set = n F n U = 19 30 Hence, the required Probability is 19 30

Construct a Venn diagram to illustrate this information: 30 students study one or more of three languages: French, German and Mandarin 5 study all three languages. 6 study Mandarin only. 2 study French and Mandarin but not German 15 students in total study Mandarin 2 study only French 3 study only German. Find n (French and Mandarin) and P (French and Mandarin) from your diagram.

We need to construct a Venn Diagram based on the given information It is given that 30 students study one or more of three languages: French, German and Mandarin. Let us draw a rectangle representing the universal set of all languages. And, let us draw three circles representing the languages French F , German G and Mandarin M . It is given that 5 study all three languages, so we have Further, it is given that 6 study only Mandarin, 2 study French and Mandarin but not German, So, we have It is given that 15 students in total study Mandarin So, the number of students studying Mandarin and German = 15 - 5 + 2 + 6 = 15 - 13 = 2 Now, it is given that 2 study only french and 3 study only German. So, we have Now, it is given that total 30 students study these three languages. So, the number of students studying French and German = 30 - 5 + 2 + 2 + 6 + 2 + 3 = 30 - 20 = 10 Hence, the Venn Diagram representation of the given information is as follows: Thus, we have Total number of students in the universal set = 30 And, from the above diagram, the number of students studying both French and Mandarin = n F ∩ M = 2 Thus, the probability that student picked up studies French and Mandarin = Number of students who study French and Mandarin Total number of students in the universal set = n F ∩ M n U = 2 30 = 1 15 Hence, the required Probability is 1 15 .

Construct a Venn diagram to illustrate this information: 30 students study one or more of three languages: French, German and Mandarin 5 study all three languages. 6 study Mandarin only. 2 study French and Mandarin but not German 15 students in total study Mandarin 2 study only French 3 study only German. Explain how you can find P ( French ∩ German ∩ Mandarin ) from your Venn diagram.

We need to construct a Venn Diagram based on the given information It is given that 30 students study one or more of three languages: French, German and Mandarin. Let us draw a rectangle representing the universal set of all languages. And, let us draw three circles representing the languages French F , German G and Mandarin M . It is given that 5 study all three languages, so we have Further, it is given that 6 study only Mandarin, 2 study French and Mandarin but not German, So, we have It is given that 15 students in total study Mandarin So, the number of students studying Mandarin and German = 15 - 5 + 2 + 6 = 15 - 13 = 2 Now, it is given that 2 study only french and 3 study only German. So, we have Now, it is given that total 30 students study these three languages. So, the number of students studying French and German = 30 - 5 + 2 + 2 + 6 + 2 + 3 = 30 - 20 = 10 Hence, the Venn Diagram representation of the given information is as follows: Thus, we have Total number of students in the universal set = 30 And, from the above diagram, the number of students who studies French, German and Mandarin = n F ∩ G ∩ M = 5 Thus, the probability that student picked up studies French, German and Mandarin = P ( French ∩ German ∩ Mandarin ) = Number of students who study French, German and Mandarin Total number of students in the universal set = n F ∩ G ∩ M n U = 5 30 = 1 6 Hence, the required Probability is 1 6 .

Construct a Venn diagram to illustrate this information: 30 students study one or more of three languages: French, German and Mandarin 5 study all three languages. 6 study Mandarin only. 2 study French and Mandarin but not German 15 students in total study Mandarin 2 study only French 3 study only German. Find: P ( F ) , P F ∩ G , P G , P ( G ∩ M ) , P ( M ) , P ( F ∩ G ∩ M ) , and P ( F ∩ M ) .

We need to construct a Venn Diagram based on the given information It is given that 30 students study one or more of three languages: French, German and Mandarin. Let us draw a rectangle representing the universal set of all languages. And, let us draw three circles representing the languages French F , German G and Mandarin M . It is given that 5 study all three languages, so we have Further, it is given that 6 study only Mandarin, 2 study French and Mandarin but not German, So, we have It is given that 15 students in total study Mandarin So, the number of students studying Mandarin and German = 15 - 5 + 2 + 6 = 15 - 13 = 2 Now, it is given that 2 study only french and 3 study only German. So, we have Now, it is given that total 30 students study these three languages. So, the number of students studying French and German = 30 - 5 + 2 + 2 + 6 + 2 + 3 = 30 - 20 = 10 Hence, the Venn Diagram representation of the given information is as follows: Thus, we have Total number of students in the universal set = n U = 30 Now, n F = 2 + 2 + 5 + 10 = 19 , n M = 6 + 2 + 2 + 5 = 15 , n G = 5 + 2 + 3 + 10 = 20 Thus, P F = n F n U = 19 30 P F ∩ G = n F ∩ G n U = 10 30 = 1 3 P G = n G n U = 3 30 = 1 10 P G ∩ M = n G ∩ F n U = 2 30 = 1 15 P M = n M n U = 6 30 = 1 5 P F ∩ G ∩ M = 5 30 = 1 6 P F ∩ M = 2 30 = 1 15

Construct a Venn diagram to illustrate this information: 30 students study one or more of three languages: French, German and Mandarin 5 study all three languages. 6 study Mandarin only. 2 study French and Mandarin but not German 15 students in total study Mandarin 2 study only French 3 study only German. Find n French ∪ Mandarin and P French ∪ Mandarin from your Venn diagram.

We need to construct a Venn Diagram based on the given information It is given that 30 students study one or more of three languages: French, German and Mandarin. Let us draw a rectangle representing the universal set of all languages. And, let us draw three circles representing the languages French F , German G and Mandarin M . It is given that 5 study all three languages, so we have Further, it is given that 6 study only Mandarin, 2 study French and Mandarin but not German, So, we have It is given that 15 students in total study Mandarin So, the number of students studying Mandarin and German = 15 - 5 + 2 + 6 = 15 - 13 = 2 Now, it is given that 2 study only french and 3 study only German. So, we have Now, it is given that total 30 students study these three languages. So, the number of students studying French and German = 30 - 5 + 2 + 2 + 6 + 2 + 3 = 30 - 20 = 10 Hence, the Venn Diagram representation of the given information is as follows: Thus, we have Total number of students in the universal set = n U = 30 Now, n F = 2 + 2 + 5 + 10 = 19 , n M = 6 + 2 + 2 + 5 = 15 Thus, n F ∪ M = n F + n M - n F ∩ M = 19 + 15 - 7 = 34 - 7 = 27 Now, P French ∪ Mandarin = n F U M n U = 27 30 = 9 10

MEDIUM

MYP:4-5

IMPORTANT

Earn 100

What are independent events?

Important Questions on Independent Events and Conditional Probability

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Probabilities of combined events>Q ●

What is conditional probability?

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Exploration 1>Q 1

Construct a Venn diagram to illustrate this information:

$30$ students study one or more of three languages: French, German and Mandarin
$5$ study all three languages.
$6$ study Mandarin only.
$2$ study French and Mandarin but not German
$15$ students in total study Mandarin
$2$ study only French
3 study only German.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Exploration 1>Q 2

Construct a Venn diagram to illustrate this information:

$30$ students study one or more of three languages: French, German and Mandarin
$5$ study all three languages.
$6$ study Mandarin only.
$2$ study French and Mandarin but not German
$15$ students in total study Mandarin
$2$ study only French
3 study only German.

From your diagram, find $n (F r e n c h)$ and $n (U)$ . Use these to find the probability that a student picked at random studies French.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Exploration 1>Q 3

Construct a Venn diagram to illustrate this information:

$30$ students study one or more of three languages: French, German and Mandarin
$5$ study all three languages.
$6$ study Mandarin only.
$2$ study French and Mandarin but not German
$15$ students in total study Mandarin
$2$ study only French
3 study only German.

Find $n$ (French and Mandarin) and $P$ (French and Mandarin) from your diagram.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Exploration 1>Q 4

Construct a Venn diagram to illustrate this information:

$30$ students study one or more of three languages: French, German and Mandarin
$5$ study all three languages.
$6$ study Mandarin only.
$2$ study French and Mandarin but not German
$15$ students in total study Mandarin
$2$ study only French
3 study only German.

Explain how you can find $P (French \cap German \cap Mandarin)$ from your Venn diagram.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Exploration 1>Q 5

Construct a Venn diagram to illustrate this information:

$30$ students study one or more of three languages: French, German and Mandarin
$5$ study all three languages.
$6$ study Mandarin only.
$2$ study French and Mandarin but not German
$15$ students in total study Mandarin
$2$ study only French
3 study only German.

Find: $P (F), P (F \cap G),$ $P (G), P (G \cap M), P (M), P (F \cap G \cap M),$ and $P (F \cap M)$ .

HARD

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Exploration 1>Q 6

Construct a Venn diagram to illustrate this information:

$30$ students study one or more of three languages: French, German and Mandarin
$5$ study all three languages.
$6$ study Mandarin only.
$2$ study French and Mandarin but not German
$15$ students in total study Mandarin
$2$ study only French
3 study only German.

Find $n (French \cup Mandarin)$ and $P (French \cup Mandarin)$ from your Venn diagram.

MEDIUM

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 5 - Independent Events and Conditional Probability>Practice 1>Q 1

A fair six-sided die has the digits $1, 2, 3, 4, 5, 6$ on its faces.

Question Image

A fair four-sided die has the digits $1, 2, 3, 4$ on its faces.

The two dice are rolled simultaneously. The diagram represents the sample space of the possible outcomes.

Let $A$ be the event 'rolling a $1$ on the four-sided die', and $B$ be the event 'rolling a $1$ on the six-sided die. Find $P (A \cap B)$ , the probability that you roll a $1$ on the four-sided die and a $1$ on the six-sided die.

What are independent events?

Important Questions on Independent Events and Conditional Probability

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