Question

The Arizona pick 6 "Lotto" lottery says you're a winner if your letter ticket has 3,4,5, or 6 of the winning numbers (of 42 to choose from). If you buy one lottery ticket, what is the probability that your ticket is a loser? PLEASE explain and show how you did this step by step. IM TRYING to actually learn how to do this problem.

Answer 1

Number of ways to choose 6 numbers from 42 numbers =

= 42! / ((42-6)! 6!)

= 42! / (36! 6!)

= (42 * 41 * 40 * 39 * 38 * 37) / (6 * 5 * 4 * 3 * 2 * 1)

= 5245786

Number of ways to have 0 winning numbers = Number of ways to choose 0 winning numbers from 6 * Number of ways to choose 6 non-winning numbers from 36

=

= 1 * 1947792

= 1947792

Number of ways to have one winning numbers = Number of ways to choose one winning numbers from 6 * Number of ways to choose five non-winning numbers from 36

=

= 6 * 376992

= 2261952

Number of ways to have two winning numbers = Number of ways to choose two winning numbers from 6 * Number of ways to choose four non-winning numbers from 36

=

= 15 * 58905

= 883575

Total number of non-winning numbers = 1947792 + 2261952 + 883575 = 5093319

Probability that your ticket is a loser = Total number of non-winning numbers / Total possible numbers

= 5093319 / 5245786

= 0.9709353