Problema Solution
To play a certain lottery, a person has to correctly select 5 out of 55 numbers, paying $1 for each five number selection. if the five numbers are the as as the ones drawn by the lottery, mountains of money are bestowed.
What is the probability that a person with one combination of five numbers will win?
what is the probability of winning if 100 different lottery tickets are purchased?
Answer provided by our tutors
the probability that a person with one combination of five numbers will win is
P (one combination of five numbers will win) = 1/ 55C5
the number of 5-combinations of 55 elements is 55C5 = 55! / (5!*50!)
55C5 = 51*52*53*54*55/(2*3*4*5)
55C5 = 3478761
P (one combination of five numbers will win) = 1/3478761 = 0.0000000287
the probability of winning if 100 different lottery tickets are purchased
P (100 different lottery tickets are purchased) = 100/ 55C5
P (100 different lottery tickets are purchased) = 100/3478761
P (100 different lottery tickets are purchased) = 0.00000287