For the lottery described in Exercise 2.4-13, find the

Solution 14E

Step1 of 3:

We have lottery game in that a particular lottery, 1/10 of the 50 million tickets will win a prize.

That is p =

               = 0.1.

We need to find,

The smallest number of tickets that must be purchased so that the probability of winning at least one prize is greater than (a) 0.50; (b) 0.95.

Step2 of 3:

Let “X” be random variable which follows binomial distribution with parameters n and p.

That is X B(n, p)

The probability mass function of binomial distribution is given below

P(X) = nCx , x = 0,1,2,...,n.

Where,

X = random variable

n = sample size

p = probability of success(or proportion).

a).

Consider,

P(X1) > 0.50

1 - P(X1) > 0.50

1 - P(X = 0) > 0.50