Question

A local lottery is conducted weekly by choosing five chips atrandom and without replacement from a population of 40 chips,numbered 1 through 40; order does not matter. the winning numbersare announced on five successive commercials during the Mondaynight broadcast of a televised movie. Suppose the first threewinning numbers mathc three of yours. What are your chances at thatpoint of winning the lottery?

Answer 1

0.002

Explanation:

The order of choosing the 5 chips without replacement from a population of 40 chips does not matter, so I decide to choose 3 chips first which match the winning numbers

Number of chips left = 40 - 3 = 37, number of chips left to be chosen = 5 - 3 = 2

The number of ways to choose the remaining 2 chips from the 37 chips left can be done by the combination method

Number of ways = n combination r = n!/(n - r)!r!

n = 37, r = 2

Number of ways = 37!/(37-2)!2! = 37!/35!2! = 37×36×35!/35!×2 = 37×36/2 = 37×18 = 666

My chances of winning = 1/666 = 0.002

Answer 2

Explanation:

five chips are chosen at random and without replacement from a population of 40 chips

First 3 chips match mine

As selection is without replacement,remaining population is 40-3=37

Remaining number of selections to be made=5-3=2

Number of possible way the two numbers can be selected is given by computing combinations without replacement.

Number of possible combinations=37!/(37-2)!2! =666

My chances=1/666=1.5*10^-3