Fatima will enter three sporting events at the weekend. Her chances of winning each of them are shown in the following table. Event Shot put Javelin Discus Chance of winning 85 % 40 % 64 % The three events are independent. What does 'the three events are independent' mean here? Give a reason why this may not be true in real life.

It means that the outcome of any of these three sporting events has no effect on the probabilities of the outcomes of the other two sporting events. This may not be true because, for example, winning one event may increase an athlete's confidence, so that they are more likely to win another event. Mathematically, A and B are said to be independent, if the outcome of one event does not affect other.

Letters and packages can take up to 2 days to be delivered by Speed post couriers. The following table shows the percentage of items delivered at certain times after sending. Same day After 1 day After 2 days Letter 40 % 50 % 10 % Package 15 % 55 % 30 % Is there any truth in the statement 'If you post 10 letters on Monday then only nine of them will be delivered before Wednesday'? Give a reason for your answer.

Probability that a letter is delivered same day = 0 . 4 Probability that a letter is delivered after one day = 0 . 5 Probability that a letter is delivered after two days = 0 . 1 Probability that a package is delivered same day = 0 . 15 Probability that a package is delivered after one day = 0 . 55 Probability that a package is delivered after two days = 0 . 3 If we post letter on Monday, probability that letter will be delivered before Wednesday i.e., probability letter is delivered same day or after one day = 0 . 4 + 0 . 5 = 0 . 9 Expectation of ten letters to be delivered before Wednesday, when posted on Monday = 10 × 0 . 9 = 9 . So, the average number of letters delivered before Wednesday are nine. But it is not true that nine letters will be definitely delivered on Wednesday. Therefore, given statement is not true.

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On any particular day, there is a $30 %$ chance of snow in Slushly. Find the probability that it snows there on:

exactly one of the next $3$ days.

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Important Questions on Probability

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Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 7

Fatima will enter three sporting events at the weekend. Her chances of winning each of them are shown in the following table.

Event	Shot put	Javelin	Discus
Chance of winning	$85 %$	$40 %$	$64 %$

Assuming that the three events are independent, find the probability that Fatima wins:

the shot put and discus

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AS and A Level

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Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 7

Fatima will enter three sporting events at the weekend. Her chances of winning each of them are shown in the following table.

Event	Shot put	Javelin	Discus
Chance of winning	$85 %$	$40 %$	$64 %$

Assuming that the three events are independent, find the probability that Fatima wins:

the shot put and discus only

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 7

Fatima will enter three sporting events at the weekend. Her chances of winning each of them are shown in the following table.

Event	Shot put	Javelin	Discus
Chance of winning	$85 %$	$40 %$	$64 %$

Assuming that the three events are independent, find the probability that Fatima wins:

exactly two of these events.

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 7

Fatima will enter three sporting events at the weekend. Her chances of winning each of them are shown in the following table.

Event	Shot put	Javelin	Discus
Chance of winning	$85 %$	$40 %$	$64 %$

The three events are independent.

What does 'the three events are independent' mean here? Give a reason why this may not be true in real life.

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AS and A Level

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Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 8

A fair six-sided spinner, $P$ , has edges marked $0, 1, 2, 2, 3$ and $4 .$
A fair four-sided spinner, $Q$ , has edges marked $0, - 1, - 1$ and $- 2 .$

Each spinner is spun once and the numbers on which they come to rest are added together to give the score, $S$ . Find:

$P (S = 2)$

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AS and A Level

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Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 8

A fair six-sided spinner, $P$ , has edges marked $0, 1, 2, 2, 3$ and $4 .$
A fair four-sided spinner, $Q$ , has edges marked $0, - 1, - 1$ and $- 2 .$

Each spinner is spun once and the numbers on which they come to rest are added together to give the score, $S$ . Find:

$P (S^{2} = 1)$

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Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 9

Letters and packages can take up to $2$ days to be delivered by Speed post couriers. The following table shows the percentage of items delivered at certain times after sending.

	Same day	After $1$ day	After $2$ days
Letter	$40 %$	$50 %$	$10 %$
Package	$15 %$	$55 %$	$30 %$

Is there any truth in the statement 'If you post $10$ letters on Monday then only nine of them will be delivered before Wednesday'? Give a reason for your answer.

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 4 - Probability>EXERCISE 4C>Q 9

Letters and packages can take up to $2$ days to be delivered by Speedipost couriers. The following table shows the percentage of items delivered at certain times after sending.

	Same day	After $1$ day	After $2$ days
Letter	$40 %$	$50 %$	$10 %$
Package	$15 %$	$55 %$	$30 %$

Find the probability that when three letters are posted on Monday, none of them are delivered on Tuesday.

On any particular day, there is a 30% chance of snow in Slushly. Find the probability that it snows there on: exactly one of the next 3 days.

Important Questions on Probability

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On any particular day, there is a $30 %$ chance of snow in Slushly. Find the probability that it snows there on:

exactly one of the next $3$ days.