Question

1. (a) A committee of 6 people is to be chosen at random in a Club which has a membership of 20 men and 30 women. What is the probability that 6 marks 6 marks 8 marks] (b) In a factory there are three machines which produce bolts. Machine A pro- duces 50% of the bolts and of these 2% are faulty. Machine B produces 20% of the bolts and of these 1.5% are faulty, and Machine C produces 30% of the bolts and of these 1% are faulty. If a bolt is selected at random from the output of the factory, and it is found to be faulty, what then is the probability 13 marks i. the committee will consist of 6 women? ii. the committee will have at least one man? iii the committee will consist of 3 women and 3 men? that it was produced by machine B?

Answer 1

1 a) Total number of people is

Number of ways in which 6 can be chosen is

i) Number of ways in which 6 women can be chosen is

So the probability of choosing 6 women is

ii) The probability of choosing at least one man is equal to 1 - the probability of no man that is all are women

So using i) we get

Required probability as

iii) Number of ways of choosing 3 men and 3 women is

Hence required probability is

b) Using Bayes's theorem we get the required probability as