Probability

The probability that it rains is 0.3. If it rains, the probability that a bus is late is 0.4; otherwise it is 0.1. Calculate the probability that a bus is late.

Given that a bus is late, calculate the probability that it rains.

20% of seeds fail to germinate. Ten seeds are planted. The number of seeds that fail to germinate, X, follows a binomial distribution B(10, 0.2). Calculate P(X = 2).

A biased coin lands on heads with probability 0.62. Calculate the expected number of times in 250 trials (probability 0.62).

In a group of 50 students, 28 study football, 22 study tennis and 9 study both (data are illustrative, written for this paper). How many study neither?

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

The heights of adult men in a town are normally distributed with mean 170 and standard deviation 8 (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 162 and 186.

A spinner lands on red with probability 0.25. It is spun 8 times. The number of successes X follows a binomial distribution B(8, 0.25). Calculate P(X = 3).

A dice is rolled 300 times and lands on six 72 times. Compare the experimental probability with the theoretical probability and comment on fairness.

The table shows how 150 students travel to school (data are illustrative, written for this paper):

	Walk	Bus	Car
Boys	24	30	16
Girls	20	38	22

A student is chosen at random. Find (i) P(Girls); (ii) P(Bus | Girls); (iii) P(Boys | Walk).