6.(vii)    Two dice are thrown. The events A, B and C are as follows:

            A: getting an even number on the first die.

            B: getting an odd number on the first die. 

            C: getting the sum of the numbers on the dice  \leq 5 

             Describe the events

              (vii) B and C

Answers (1)

Sample space when two dice are thrown:

S = {(x,y): 1 \leq x,y \leq 6}

B: getting an odd number on the first die = {(a,b): a \in {1,3,5} and 1 \leq b \leq 6}

 = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)}

C: getting the sum of the numbers on the dice \leq 5 

The possible sum are 2,3,4,5

C = {(a,b):  2 \leq a + b \leq 5} = {(1, 1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1)}

(vi) B and C = B \cap C = {(1, 1), (1,2), (1,3), (1,4), (3,1), (3,2)}

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