Question

In a lottery game, a player picks 5 numbers from 1 to 46. If 4 of the 5 numbers match those drawn, the player wins second prize. What is the probability of winning this prize? Be sure to leave your answer as a fraction in order to earn credit.

Answer 1

Explanation:

given that in a lottery game, a player picks 5 numbers from 1 to 46

If 4 of the 5 numbers match those drawn, the player wins second prize.

Assuming the numbers are chosen without repitition we find that the player can choose 5 numbers in 46C5 ways.

To win the prize he must choose 4 numbers form the 5 numbers in the prize and remaining 1 number any other number.

i.e. no of ways to get II price = choosing 4 numbers out of 5, and one number from 41

=
`5C4*41C1 = 205`

Probability of winning this prize

=
`(205)/(46C5) \\= (205*5(4)(3)(2)1)/(46*45*44*43*42) \\=(41*5*2*3)/(46*9*22*43*21) \\=(205)/(1370754)`