MEDIUM
AS and A Level
IMPORTANT
Earn 100
A biased coin is four times as likely to land heads up compared with tails up. The coin is tossed times so that the probability that it lands tails up on at least one occasion is greater than . Find the least possible value of .
Important Questions on The Binomial and Geometric Distributions
MEDIUM
AS and A Level
IMPORTANT
Given that and that , express the constant in terms of , and find the smallest value of for which .
MEDIUM
AS and A Level
IMPORTANT
A book publisher has noted that, on average, one page in eight contains at least one spelling error, one page in five contains at least one punctuation error, and that these errors occur independently and at random. The publisher checks randomly selected pages from various books for errors. How many pages are expected to contain at least one of both types of error?
MEDIUM
AS and A Level
IMPORTANT
A book publisher has noted that, on average, one page in eight contains at least one spelling error, one page in five contains at least one punctuation error, and that these errors occur independently and at random. The publisher checks randomly selected pages from various books for errors. Find the probability that: the first spelling error occurs after the th page
MEDIUM
AS and A Level
IMPORTANT
A book publisher has noted that, on average, one page in eight contains at least one spelling error, one page in five contains at least one punctuation error, and that these errors occur independently and at random. The publisher checks randomly selected pages from various books for errors. Find the probability that: the first punctuation error occurs before th page
MEDIUM
AS and A Level
IMPORTANT
A book publisher has noted that, on average, one page in eight contains at least one spelling error, one page in five contains at least one punctuation error, and that these errors occur independently and at random. The publisher checks randomly selected pages from various books for errors. Find the probability that: th page is the first to contain both types of error.
MEDIUM
AS and A Level
IMPORTANT
Robert uses his calculator to generate random integers between and inclusive. Find the probability that at least of the integers are less than or equal to
MEDIUM
AS and A Level
IMPORTANT
Robert generates random integers between and inclusive. The random variable is the number of these integers which are less than or equal to a certain integer between and inclusive. It is given that the mean of is and the variance of is .Find the values of and .
HARD
AS and A Level
IMPORTANT
Anna, Bel and Chai take turns, in that order, at rolling an ordinary fair die. The first person to roll a wins the game. Find the ratio ( Anna wins) Bel wins) (Chai wins), giving your answer in its simplest form.
