Question

. Forty-four states, Washington D.C., and the Virgin Islands have joined for the Mega Millions lottery game. For this game the player selects five white balls numbered from 1 to 70, inclusive, plus a single gold Mega Ball numbered from 1 to 25, inclusive. There are several different prize options including the following. (a) What is the probability of matching all five white balls plus the Mega Ball and winning the jackpot? (b) What is the probability of matching five white balls but not the Mega Ball and winning $1,000,000? (c) What is the probability of matching four white balls plus the Mega Ball and winning $10,000? (d) What is the probability of matching four white balls but not the Mega Ball and winning $500? (e) What is the probability of matching the Mega Ball only and winning $2?

Answer 1

a)probability of matching all five white balls plus the Mega Ball and winning the jackpot

=((⁵C₅)*(⁶⁵C₀)/(⁷⁰C₅))*(1/25) =(1*1/12103014)*(1/25)=1/302575350

b)

probability of matching five white balls but not the Mega Ball and winning $1,000,000

=((⁵C₅)*(⁶⁵C₀)/(⁷⁰C₅))*(24/25) =(1*1/12103014)*(24/25)=24/302575350=1/12607306

c)

probability of matching four white balls plus the Mega Ball and winning $10,000

=((⁵C₄)*(⁶⁵C₁)/(⁷⁰C₅))*(1/25) =(5*65/12103014)*(1/25)=1/931001

d)

probability of matching four white balls but not the Mega Ball and winning $500:

=((⁵C₄)*(⁶⁵C₁)/(⁷⁰C₅))*(24/25) =(5*65/12103014)*(24/25)=52/2017169

e) probability of matching the Mega Ball only and winning $2

(⁵C₀)*(⁶⁵C₅)/(⁷⁰C₅))*(1/25)=196664/7204175