In one type of lottery 5 distinct numbers are picked at once from 1, ..., 40...

In one type of lottery 5 distinct numbers are picked at once from 1, ..., 40 uniformly at random.

a. Describe the sample space and P to model this experiment.

b. What is the probability that out of the 5 picked numbers exactly 3 will be even?

Solutions

Expert Solution

(a) Sample space, S = {(x1,x2,x3,x4,x5) such that xi = 1,2,..., 40; i = 1,2,3,4,5}.
Probability, P = P({(x1,x2,x3,x4,x5) such that xi = 1,2,..., 40; i = 1,2,3,4,5}) = 1

(b) Event, A = 3 numbers are even, 2 numbers are odd.
There are 20 even numbers and 20 odd numbers.
Hence, Prob.(A) = = 0.329

orchestra answered 1 year ago

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