Question

two unbiased dice are thrown consider the following events
A: Getting a prime number on both sides
B: Sum of the numbers is an odd number

(a) describe A in rooster form
(b) find P(A) and P(B)
(c) find P(A intersection B) and
P((A intersection B)')​

Answer 1

Sample space when two dies are thrown is,
{ (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
There are total 36 possible cases out of which favorable cases i.e. getting both prime numbers are { (2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)}
Probability = n(favorable cases)/n(sample space)
Probability = 9/36 = 1/4