MEDIUM
AS and A Level
IMPORTANT
Earn 100
When a certain driver parks their car in the evenings, they are equally likely to remember or to forget to switch off the headlights. Find the probability that on the next occasions that they park their car in the evening, they forget to switch off the headlights: more times than they remember to switch them off
Important Questions on The Binomial and Geometric Distributions
MEDIUM
AS and A Level
IMPORTANT
When a certain driver parks their car in the evenings, they are equally likely to remember or to forget to switch off the headlights. Find the probability that on the next occasions that they park their car in the evening, they forget to switch off the headlights: at least more times than they remember to switch them off.
MEDIUM
AS and A Level
IMPORTANT
Gina has been observing students at a university. Her data indicate that of the males and of the females are wearing earphones at any given time. She decides to interview randomly selected students and to interview males and females alternately. Use Gina's observation data to find the probability that the first person not wearing earphones is the third male interviewed, given that she first interviews: a male
MEDIUM
AS and A Level
IMPORTANT
Gina has been observing students at a university. Her data indicate that of the males and of the females are wearing earphones at any given time. She decides to interview randomly selected students and to interview males and females alternately. Use Gina's observation data to find the probability that the first person not wearing earphones is the third male interviewed, given that she first interviews: a female and state any assumptions made about the wearing of earphones in your calculations
MEDIUM
AS and A Level
IMPORTANT
Gina has been observing students at a university. Her data indicate that of the males and of the females are wearing earphones at any given time. She decides to interview randomly selected students and to interview males and females alternately. Use Gina's observation data to find the probability that the first person not wearing earphones is the third male interviewed, given that she first interviews: a male who is wearing earphones. and state any assumptions made about the wearing of earphones in your calculations
MEDIUM
AS and A Level
IMPORTANT
In Restaurant Bijoux of customers rated the food as 'poor', of customers rated the food as 'satisfactory' and rated it as 'good'. A random sample of customers who went for a meal at Restaurant Bijoux was taken. Find the probability that more than and fewer than of them rated the food as 'good'.
MEDIUM
AS and A Level
IMPORTANT
In Restaurant Bijoux of customers rated the food as 'poor', of customers rated the food as 'satisfactory' and rated it as 'good'. On a separate occasion, a random sample of customers who went for a meal at the restaurant was taken. Find the smallest value of for which the probability that at least person will rate the food as 'poor' is greater than .
MEDIUM
AS and A Level
IMPORTANT
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 .
MEDIUM
AS and A Level
IMPORTANT
Given that and that , express the constant in terms of , and find the smallest value of for which .
