Question

In a lottery game, a player picks 4 numbers from 1 to 46. If 2 of those 4 numbers match those drawn, the player wins third prize. Let's walk through the steps to determine the probability of winning third prize.

In how many ways can 2 winning numbers be chosen from the possible 4 numbers?

In how many ways can 2 non-winning numbers be chosen from the pool of all non-winning numbers?

The number of favorable outcomes would be to multiply the above two answers together, since we want 2 winning numbers and 2 non-winning numbers. What is the number of favorable outcomes?

In how many ways can you pick any 4 numbers from the pool of 46 numbers? This is your total outcomes. .

What is the probability of winning third prize? (Round to 5 decimal places.)

Answer 1

Number of ways can 2 winning numbers be chosen from the possible 4 numbers= 4!/(2!2!)=24/(2*2)=6

Number of ways can 2 non-winning numbers be chosen from the pool of all non-winning numbers= 46!/(44!2!)=(46*45)/2=1035

The number of favorable outcomes=6*1035 =6210

Number of ways we can pick 4 numbers from a pools of 46 numbers= 46!/(42!4!)= 46*45*44*43/24=163185

The probability of winning third prize =6210/163185 =0.03805