Q

# 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 ≤ 5. Describe the events (viiI) A ∩ B′ ∩ C′

6.(viii) 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

(viii) $A\cap {B}'\cap {C}'$

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Sample space when two dice are thrown:

S = {(x,y): 1 $\dpi{80} \leq$ x,y $\dpi{80} \leq$ 6}

A: getting an even number on the first die = {(a,b): a $\dpi{80} \in$ {2,4,6} and 1 $\dpi{80} \leq$ b $\dpi{80} \leq$ 6}

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

B: getting an odd number on the first die = {(a,b): a $\dpi{80} \in$ {1,3,5} and 1 $\dpi{80} \leq$ b $\dpi{80} \leq$ 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 $\dpi{80} \leq$ 5

The possible sum are 2,3,4,5

C = {(a,b):  2 $\dpi{80} \leq$ a + b $\dpi{80} \leq$ 5} = {(1, 1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1)}

(viii) A $\cap$ B' $\cap$ C' = A $\cap$ A $\cap$ C'  (from (ii))

= A $\cap$ C' = A - C = {(2,4), (2,5), (2,6), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

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