Question

The Powerball is played by selecting five numbers (without repetition) from the white balls labeled 1 through 69 (the order doesn't matter) and one red ball (the powerball) with label from 1 through 26. You win the grand prize if you get all five white numbers plus the powerball. 3. (a.) How many possible tickets are there? What is the probability of winning the grand prize? (b.) You win $4 if you get the powerball and at most one white number. What is the probability of winning $4? (c.) You win $100 if you get three white balls plus the powerball OR four white balls. What is the probability of winning $100?

Answer 1

a)

total possible tickets =N(Select 5 from 69 and select 1 red from 26)=(69C5)*(26C1) =11238513*26 =292201338

P(winning grand prize) =1/292201338

b)

P(winnning $4) =P(match 0 white and red ball)+P(match 1 white and red ball(

=(5C0)*(64C5)*(1C1)/292201338+(5C1)*(64C4)*(1C1)/292201338 =(1*7624512+5*6353376)/292201338

=10801392/292201338 =105896/2864719

c)

P(winning $100)=(5C3)*(64C2)*(1C1)/292201338+(5C4)*(64C1)*25/2922013382

=(10*2016+5*64*25)/292201338 =921/9556727