EXERCISES. 1 Shonil is practising playing darts

1 Shonil is practising playing darts. The probability that he hits the dartboard is 0.6.

a) Find the probability that he hits the dartboard at least once in four throws.

b) How many darts must he throw in order that the probability that he hits the dartboard at least once is greater that 0.99?

c) How many darts must Shonil throw in order that the probability that the dartboard is not hit is less than 0.01?

2 A die is biased such that the probability of throwing a six is 0.2.

a) Find the probability of throwing at least one six in the first eight throws.

b) How many times must the die be thrown in order that the probability of getting at least one six is greater than 0.995?

3 To proceed to the second round in a mathematics competition, Katie must get at least one of the four questions in the first round completely correct.The probability that she gets a question completely correct is 0.65. What is the probability that she proceeds to the second round?

4 Terri and Robyn are playing a game with a tetrahedral die. Terri goes first and they take turns at throwing the die. The first person to throw a one is the winner. What is the probability that Robyn wins?

5 Ayesha cycles to school. She has a choice of two routes, route A and route B. She is three times more likely to travel by route A than route B. If she travels by route A the probability that she will be late is 0.1 and if she travels by route B the probability that she will be late is 0.15. On a particular Monday Ayesha is late for school. Use Bayes’ theorem to find the probability that she travelled by route A.

Ali should take two examinations, one in mathematics and one in English. On the day of the examinations, he takes only one. He is five times more likely to take mathematics than English. If he takes mathematics the probability that he passes is 0.9 and if he takes English the probability that he passes is 0.8. Ali passes the examination. Use Bayes’ theorem to find the probability that he took mathematics.