Probability

The probability that a student passes a theory test is 0.7. If a student passes a theory test, the probability that they pass the practical is 0.8; otherwise it is 0.5. Calculate the probability that they pass the practical.

Given that they pass the practical, calculate the probability that a student passes a theory test.

Events A and B are independent. P(A) = 0.4 and P(B) = 0.35. Calculate P(A and B) and P(A or B).

A basketball player scores 70% of free throws. She takes 6 free throws. The number of successes X follows a binomial distribution B(6, 0.7). Calculate P(X = 5).

The lifetimes of light bulbs (hours) are normally distributed with mean 1200 and standard deviation 100 (data are illustrative, written for this paper). Use the fact that about 68% of values lie within 1 standard deviation of the mean, and about 95% within 2, to estimate the percentage between 1000 and 1400.

The table shows how 200 students travel to school (data are illustrative, written for this paper):

	Walk	Bus	Car
Year 10	35	42	23
Year 11	28	47	25

A student is chosen at random. Find (i) P(Year 11); (ii) P(Bus | Year 11); (iii) P(Year 10 | Walk).

A spinner lands on blue with probability 0.15. Calculate the expected number of times in 400 trials (probability 0.15).

In a group of 60 students, 35 study French, 24 study Spanish and 11 study both (data are illustrative, written for this paper). How many study neither?

A student who studies Spanish is chosen at random. Find the probability that they also study French.

Two counters are taken at random without replacement from a bag of 5 red and 3 blue counters. Calculate the probability that both are the same colour.

15% of components are faulty. A box of 12 is chosen. The number of faulty components X follows a binomial distribution B(12, 0.15). Calculate P(X = 1).

Times to complete a puzzle (minutes) are normally distributed with mean 40 and standard deviation 5 (data are illustrative, written for this paper). Use the fact that about 68% of values lie within 1 standard deviation of the mean, and about 95% within 2, to estimate the percentage between 35 and 45.

The table shows the activity chosen by 240 members of a leisure centre (data are illustrative, written for this paper):

	Swim	Gym	Classes
Adults	45	60	35
Children	55	15	30

A member is chosen at random. Find (i) P(Children); (ii) P(Gym | Children); (iii) P(Adults | Swim).

The probability that a seed germinates is 0.85. Calculate the expected number of times in 240 trials (probability 0.85).