Answer to Question #258506 in Statistics and Probability for Ahmad

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:

$P=0.1^3=0.001$

the probability of not matching any numbers on a ticket:

$P=0.9^3=0.027$

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

$P=1/C^5_{49}=\frac{44!5!}{49!}=1/1906884$

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

$P=43/C^5_{49}=43/1906884$

the probability of not matching any numbers on a ticket:

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