Question

1. A lottery consists of 50 numbers from which you pick 5 numbers without replacement and order does not matter. What is the probability that:
   1. all 5 numbers match?
   2. three of the 5 numbers match

Answer 1

a) Probability that all 5 numbers match is computed here as:
= 1 / Total number of ways to select 5 numbers from 50 numbers

Therefore 1/ 2118760 is the required probability here.

b) Probability that three of the 5 numbers match is computed here as:

= Number of ways to choose 3 numbers from the 5 numbers selected * Number of ways to select rest 2 numbers from the remaining 45 numbers / Total ways to select 5 numbers from 50 numbers

Therefore 0.0047 is the required probability here.