Answer to Question #201013 in Statistics and Probability for Allison Way

Question

Lottery games are very popular, but what are the actual probabilities that a ticket purchased is going to win? Calculate the probability of winning some of the more popular games. A game that draws 3 digits from 0-9 from three separate machines. What is the probability of winning a “box” bet by matching the three digits in any order?What is the probability of not matching any numbers on a ticket? A game that draws 5 digits from 1-49 from the same machine. In other words, numbers are drawn and not replaced. What is the probability of winning the jackpot by matching all 5 numbers?What is the probability of winning a major prize by matching 4 of the 5 numbers? Make the calculation assuming the first 4 values are matched and the fifth one does not.What is the probability of not matching any numbers on a ticket?

Answer 1

The probability of winning a “box” bet by matching the three digits in any order is :

$P=(0.1)^3=0.001$

The probability of not matching any numbers on a ticket is :

$P=(0.9)^3=0.027$

The probability of winning the jackpot by matching all 5 numbers is :

$P=\dfrac{1}{^5C_{49}}=\dfrac{44!\cdot5!}{49!}=1/1906884$

The probability of winning a major prize by matching 4 of the 5 numbers:

$P=\dfrac{43}{^5C_{49}}=43/1906884$

The probability of not matching any numbers on a ticket:

$P=\dfrac{1}{C^{5}_{44}}=\dfrac{39!\cdot5!}{44!}=1/1086008$