It is claimed that for a particular lottery, 1/10 of the 50 million tickets will win a prize. What is the probability of winning at least one prize if you purchase (a) 10 tickets or (b) 15 tickets?

Solution 13E

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 probability of winning at least one prize if you purchase

(a) 10 tickets or

(b) 15 tickets?

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).

Here we have n = 10 and p = 0.1.

The probability that at least one prize is given by

P(X1) = 1 - P(X1)

= 1 - P(X = 0) ……….(1)

Where,

P(X = 0) = 10C0 [therefore substitute x = 0, n = 10 and p = 0.1 in above pmf]

= 1(1)(0.3487)

= 0.3487.

Substitute P(X = 0) = 0.3487 in above equation (1)...