MATH 367, Fall 98, CHAPTER 3 Section 2

Bernulli trials

1. An infinite sequence of independent trials is to be performed. Each trial results in a sucess with probability p and a failure with probability q = 1 − p. What is the probability that

(a) At least 1 success occurs in the first n trials?

(b) Exactly k successes occur in the first n trials?

(c) All trials result in successes?

(d) The first trial occurs in the nth trial?

(e) It takes n trials to obtain 2 successes?

2. Suppose that each child born to a couple is equally likely to be a boy as a girl independent of the sex distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events:

(a) all children are of the same sex,

(b) the 3 eldest are boys and the 2 youngest are girls,

(c) exactly 3 are boys,

(d) the two oldest are boys,

(e) there is at least 1 girl.

3. In successive rolls of a fair die, what is the probability of getting a seven before 3 even numbers?

Assignment for Section 3.2 read section 3.2 and do problems 15–21.