Case Based Questions (MCQ)

Chapter 13 Class 12 Probability
Serial order wise

## (d) 1/60

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### Transcript

Question A coach is training 3 players. He observes that the player A can hit a target 4 times in 5 shots, player B can hit 3 times in 4 shots and the player C can hit 2 times in 3 shots. From this situation answer the following:P(A) = Probability of A hitting the target = π/π P(B) = Probability of B hitting the target = π/π P(C) = Probability of C hitting the target = π/π Question 1 Let the target is hit by A, B and C. Then, the probability that A, B and, C all will hit, is (a) 4/5 (b) 3/5 (c) 2/5 (d) 1/5P(all hit) = Probability A will hit Γ Probability B will hit Γ Probability C will hit = 4/5 Γ 3/4 Γ 2/3 = π/π So, the correct answer is (c) Question 2 Referring to (i), what is the probability that B, C will hit and A will lose? (a) 1/10 (b) 3/10 (c) 7/10 (d) 4/10P(B and C will hit and A will lose) = Probability A will not hit Γ Probability B will hit Γ Probability C will hit = (πβπ/π)"Γ" π/π Γ π/π = 1/5 Γ 3/4 Γ 2/3 = π/ππ So, the correct answer is (a) Question 3 With reference to the events mentioned in (i), what is the probability that βany two of A, B and C will hit? (a) 1/30 (b) 11/30 (c) 17/30 (d) 13/30 P(any two will hit) = P(A will not hit) Γ P(B will hit) Γ P(C will hit) + P(A will hit) Γ P(B will not hit) Γ P(C will hit) + P(A will hit) Γ P(B will hit) Γ P(C will not hit) = (1β4/5)"Γ" 3/4 Γ 2/3 + 4/5 "Γ" (1β3/4)Γ 2/3 +4/5 "Γ" 3/4 Γ (1β2/3) = 1/5 "Γ" 3/4 Γ 2/3 + 4/5 "Γ" 1/4 Γ 2/3 +4/5 "Γ" 3/4 Γ 1/3 = 1/10+2/15+1/5 = ππ/ππ So, the correct answer is (d) Question 4 What is the probability that βnone of them will hit the targetβ? (a) 1/30 (b) 1/60 (c) 1/15 (d) 2/15P(none will hit) = Probability A will not hit Γ Probability B will not hit Γ Probability C will not hit = (πβπ/π) Γ (πβπ/π)Γ(πβπ/π) = 1/5Γ1/4Γ1/3 = π/ππ So, the correct answer is (b) Question 5 What is the probability that at least one of A, B or C will hit the target? (a) 59/60 (b) 2/5 (c) 3/5 (d) 1/60P( at least one will hit) = P(exactly one will hit) + P(exactly two will hit) + P(all will hit) P(exactly one will hit) P(exactly one will hit) = P(A will hit)ΓP(B will not hit) Γ P(C will not hit) + P (A will not hit) Γ P (B will hit) Γ P (C will not hit) + P (A will not hit)Γ P (B will not hit) Γ P (C will hit) = 4/5Γ(1β3/4)Γ(1β2/3) +(1β4/5)Γ3/4Γ(1β2/3) +(1β4/5)Γ(1β3/4)Γ2/3= 4/5 "Γ" 1/4 Γ 1/3 + 1/5 "Γ" 3/4Γ 1/3 +1/5 "Γ" 1/4 Γ 2/3 = 1/15+1/20+1/30 = π/ππP(exactly two will hit) This is calculated in Question 3 P(exactly two will hit) = ππ/ππ P(all will hit) This is calculated in Question 1 P(all will hit) = π/πNow, P(at least one will hit) = P(exactly one will hit) + P(exactly two will hit) + P(all will hit) = 9/60+13/30+2/5 = ππ/ππ So, the correct answer is (a)