In a state lottery game you select six numbers from 1 to 44. the state selects six numbers at random from 1 to 44 without replacement. you must match four out of the state's six to win third prize. the order of the numbers is irrelevant. find the probability of winning third prize.

Question

Mathematics

Marcos Ayala

23 May, 06:44

In a state lottery game you select six numbers from 1 to 44. the state selects six numbers at random from 1 to 44 without replacement. you must match four out of the state's six to win third prize. the order of the numbers is irrelevant. find the probability of winning third prize.

+3

Answers (1)

Know the Answer?

Boots · Answer 1

We need to correctly choose exactly 4 out of the 6 drawn numbers.

Apply hypergeometric distribution:

a=number of correctly chosen numbers = 4

A=number of correct (drawn) numbers = 6

b=number of incorrectly chosen numbers = 2

B=number of undrawn numbers = 44-6 = 38

Then by the hypergeometric distribution

P (a, b, A, B)

=C (A, a) C (B, b) / C (A+B, a+b) [C (n, r) = combination of r objects taken out of n]

=C (6,4) C (38,2) / C (44,6)

=15*703/7059052

= 10545/7059052

= 0.001494 (to the nearest millionth)

Answer: probability of winning third prize is 10545/7059052=0.001494