Question

Question 3 An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

A: the sum is greater than 8, B: 2 occurs on either die

C: The sum is at least 7 and a multiple of 3.

Which pairs of these events are mutually exclusive?

Class X1 - Maths -Probability Page 393

Answer 1

when two dice are thrown then, there are 6 × 6 possible outcomes .
e.g., S = {(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)}

A = the sum is greater than 8
= {(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)}

B = 2 occur on the either die
= {(1,2),(2,1),(2,2),(2,3),(2,4)(2,5),(2,6),(3,2),(4,2),(5,2),(6,2)}

C = the sum is at least 7 and a multiple of 3
means the sum is 9 and 12 .
= {(3,6),(4,5),(5,4),(6,3),(6,6)}
∴ A ∩ B = Φ so, A and B are mutually exclusive.

B ∩ C = Φ so, B and C are also mutually exclusive .

Answer 2

HERE IN THIS IMAGE, I HAVE TRIED TO SHOW YOU THE PERFECT ANSWER OF THIS QUESTION.

IN THIS IMAGE M.E STANDS FOR MUTUALLY EXCLUSIVE.

I HOPE IT WILL HELP YOU.

THANK YOU