Lotteries have been a very successful money maker for governments around the wor

Question

Lotteries have been a very successful money maker for governments around the

world. In the United States, recent Powerball and Mega Millions jackpots have

run into the hundreds of millions of dollars, with many millions of people buying

tickets. (As a side note, these lotteries typically return roughly half of every dollar

wagered to the players through the prizes, with the remainder going to expenses

and government coffers.) Suppose the folks at Interprovincial Lottery Corporation,

enticed by those large jackpots in the US, want to design a lottery that is similar

to Lotto 6/49 but is much more difficult to win. (As they think it will result in

more carry-overs, larger jackpots, more news coverage, greater participation, and

greater profits for the lottery corporation.) They decide on the following rules for

the so-called Red &White lottery: four white balls will be randomly chosen from

49 numbered white balls, and, from a separate drum, 2 red balls are chosen from

49 numbered red balls. To win the grand prize, ticket buyers must pick the correct

4 white balls and 2 red balls. The order in which the balls are drawn does not

matter.

(a) On any individual drawing, what is the probability that there are no even

numbers drawn?

(b) If you buy a single ticket, what is the probability you win the grand prize?

(c) Suppose in its initial offering, 10 million tickets are sold. Assuming the num-

bers were picked purely randomly and independently, what is the probability

there is a carryover? (That is, what is the probability that nobody wins

the grand prize.) (In reality, numbers are not always picked randomly and

independently, but this assumption provides a reasonable baseline.

Explanation / Answer

a)probability that there are no even numbers drawn =P( selecting 4 white balls out of 25 odd numbered balls * selecting 2 red balls out of 25 odd numbered balls ) =((25C4)*(25C2))/((49C4)*(49C2)) =0.0152

b)probability you win the grand prize =1/((49C4)*(49C2)) =4.0134*10-9

c)

probability that nobody wins the grand prize =1- 107/((49C4)*(49C2)) =1-0.0401 =0.9599

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.