Suppose two fair dice plural are rolled Find the given proba

Suppose two fair dice (plural) are rolled. Find the given probabilities.

a) The sum is 5 or the second die shows a 3

b) Both dice show the same number, or the sum is at least 11.

Two dice are rolled

Sample space will consist of 36 elements

a) Prob for sum is 5 or Second die shows a 3

Let A = sum is 5

Fvle outcomes for A = (1,4) (2,3) (3,2( 4,1) = 4

Favourable for AB = (2,3) =1

Second die shows a 3 prob = 1/6

P(A) = 4/36

P(B)=6/36

P(AB) = 1/36

Hence Prob (sum is 5 or second die shows a 3) = P(AUB) = P(A)+P(B)_P(AB)

= 9/36 =0.25

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b) Let C = both die show the same number

D= sum is atleast 11

Favourable outcomes for C = (1,1)(2,2)...(6,6)

FAvourable outcomes for D= (5,6) (6,5) (6,6)

For both = (6,6)

Hence P(CUD) = P(C)+P(D)-P(CD)

= (6+3-1)/36 = 0.2222