Given that X ~ B n , 1 n find an expression for P X = 1 in terms of n .

Given that, X ~ B n , 1 n We have, n = n and p = 1 n If X is a discrete random variable which is binomial distributed , X ~ B ( n , p ) then the probability of obtaining r successes out of n independent trials, when p is the probability of success for each trial, is P ( X = r ) = n r p r ( 1 - p ) n - r Now, P ( X = 1 ) = n 1 1 n 1 1 - 1 n n - 1 ⇒ P X = 1 = n × 1 n × n - 1 n n - 1 ⇒ P X = 1 = n - 1 n n - 1

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AS and A Level

IMPORTANT

Earn 100

A standard deck of $52$ playing cards has an equal number of hearts, spades, clubs and diamonds. A deck is shuffled and a card is randomly selected. Let $X$ be the number of cards selected, up to and including the first diamond. Find the probability that: $X$ is equal to $E (X)$

Important Questions on The Binomial and Geometric Distributions

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 8

A standard deck of

52

playing cards has an equal number of hearts, spades, clubs and diamonds. A deck is shuffled and a card is randomly selected. Let

X

be the number of cards selected, up to and including the first diamond. Find the probability that: neither of the first two cards selected is a heart and the first diamond is the third card selected.

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AS and A Level

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Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 9

A study reports that a particular gene in

0.2 %

of all people is defective.

X

is the number of randomly selected people, up to and including the first person that has this defective gene. Given that

P (X \leq b) > 0.865

, find

E (X)

and find the smallest possible value of

b

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 10

Anouar and Zane play a game in which they take turns at tossing a fair coin. The first person to toss heads is the winner. Anouar tosses the coin first, and the probability that he wins the game is

0 . 5^{1} + 0 . 5^{3} + 0 . 5^{5} + 0 . 5^{7} + \dots

Find the probability that Zane wins the game.

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>EXERCISE 7D>Q 10

Anouar and Zane play a game in which they take turns at tossing a fair coin. The first person to toss heads is the winner. Anouar tosses the coin first, and the probability that he wins the game is

0 . 5^{1} + 0 . 5^{3} + 0 . 5^{5} + 0 . 5^{7} + \dots

Describe the sequence of results represented by the value

0 . 5^{5}

in this series. Find the probability that Anouar wins the game.

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AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>END-OF-CHAPTER REVIEW EXERCISE 7>Q 1

Given that

X ~ B (n, \frac{1}{n})

find an expression for

P (X = 1)

in terms of

n

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>END-OF-CHAPTER REVIEW EXERCISE 7>Q 2

A family has booked a long holiday in Skragness, where the probability of rain on any particular day is

0.3

. Find the probability that: the first day of rain is on the third day of their holiday

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>END-OF-CHAPTER REVIEW EXERCISE 7>Q 2

A family has booked a long holiday in Skragness, where the probability of rain on any particular day is

0.3

. Find the probability that: it does not rain for the first

2

weeks of their holiday.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 7 - The Binomial and Geometric Distributions>END-OF-CHAPTER REVIEW EXERCISE 7>Q 3

One plastic robot is given away free inside each packet of a certain brand of biscuits. There are four colours of plastic robot (red, yellow, blue and green) and each colour is equally likely to occur. Nick buys some packets of these biscuits. Find the probability that he gets a green robot on opening his first packet,

A standard deck of 52 playing cards has an equal number of hearts, spades, clubs and diamonds. A deck is shuffled and a card is randomly selected. Let X be the number of cards selected, up to and including the first diamond. Find the probability that: X is equal to EX

Important Questions on The Binomial and Geometric Distributions

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A standard deck of $52$ playing cards has an equal number of hearts, spades, clubs and diamonds. A deck is shuffled and a card is randomly selected. Let $X$ be the number of cards selected, up to and including the first diamond. Find the probability that: $X$ is equal to $E (X)$