JAMIA 2021 — Mathematics PYQ

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Question

JAMIA 2021 — Mathematics PYQ

JAMIA | Mathematics | 2021

Three persons A, B and C fire at a target in turn, starting with A. Their probabilities of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is:

Choose the correct answer:

Explanation

1. Given Probabilities:

P(A) = 0.4, \quad P(A') = 0.6

P(B) = 0.3, \quad P(B') = 0.7

P(C) = 0.2, \quad P(C') = 0.8

2. Possible Cases for Exactly Two Hits:

Case 1: A and B hit, C misses $\to P(A) \cdot P(B) \cdot P(C')$
Case 2: A and C hit, B misses $\to P(A) \cdot P(B') \cdot P(C)$
Case 3: B and C hit, A misses $\to P(A') \cdot P(B) \cdot P(C)$

3. Calculation of Cases:

P(\text{Case 1}) = 0.4 \times 0.3 \times 0.8 = 0.096

P(\text{Case 2}) = 0.4 \times 0.7 \times 0.2 = 0.056

P(\text{Case 3}) = 0.6 \times 0.3 \times 0.2 = 0.036

4. Total Probability:

P(\text{Two hits}) = 0.096 + 0.056 + 0.036

P(\text{Two hits}) = 0.188

Final Answer:

The probability of two hits is:

0.188

Choose the correct answer:

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