Question

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.

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