Two dice are rolled once. Find the probability of getting an even number on the first die, or a total of 7. -Maths 9th

Two dice are rolled once. Find the probability of getting an even number on the first die, or a total of 7. -Maths 9th
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1 Answer

Answer :

(c) \(rac{7}{12}\)Total number of ways in which 2 dice are rolled = 6 × 6 = 36 ⇒ n(S) = 36 Let A : Event of rolling an even number of 1st dice B : Event of rolling a total of 7 ⇒ A = {(2, 1), (2, 2)…, (2, 6), (4, 1), (4, 2) …, (4, 6), (6, 1), (6, 2), …, (6, 6)} and B = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)} ⇒ n(A) = 3 × 6 = 18, n(B) = 6 ⇒ A ∩ B : Event of rolling an even number on 1st dice and a total of 7 ⇒ A ∩ B = {(2, 5), (4, 3), (6, 1)} ⇒ n(A ∩ B) = 3 ∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{18}{36}\);  P(B) = \(rac{n(B)}{n(S)}\) = \(rac{6}{36}\); P(A\(\cap\)B) = \(rac{3}{36}\)⇒ P(A ∪ B) = P(Event of rolling an even number 1st dice or a total of 7) = P(A) + P(B) – P(A ∩ B)= \(rac{18}{36}\) + \(rac{6}{36}\) - \(rac{3}{36}\) = \(rac{21}{36}\) = \(rac{7}{12}\).
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