EASY
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. Given that X follows a geometric distribution, describe the way in which the cards are selected, and give the reason for your answer.

Important Questions on The Binomial and Geometric Distributions

MEDIUM
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: X is equal to EX
MEDIUM
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.
MEDIUM
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 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 PX≤b>0.865, find EX and find the smallest possible value of b.
MEDIUM
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 0.51+0.53+0.55+0.57+… Find the probability that Zane wins the game.
MEDIUM
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 0.51+0.53+0.55+0.57+… Describe the sequence of results represented by the value 0.55 in this series. Find the probability that Anouar wins the game.
MEDIUM
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~Bn,1n find an expression for PX=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.