Test Index

Probability

Question : 106 of 127

Marks: +1, -0

C 4

a

Solution:

Concept:

Probability of exactly two hits from three independent events.

Explanation:

Let

P(A) = \frac{2}{5}

P(B) = \frac{3}{5}

P(C) = \frac{4}{5}

Missing probabilities:

P(A') = \frac{3}{5}

P(B') = \frac{2}{5}

P(C') = \frac{1}{5}

Exactly two hits occur in three cases:

1. A and B hit, C misses:

\frac{2}{5} \times \frac{3}{5} \times \frac{1}{5} = \frac{6}{125}

2. A and C hit, B misses:

\frac{2}{5} \times \frac{4}{5} \times \frac{2}{5} = \frac{16}{125}

3. B and C hit, A misses:

\frac{3}{5} \times \frac{4}{5} \times \frac{3}{5} = \frac{36}{125}

Sum:

\frac{6}{125} + \frac{16}{125} + \frac{36}{125} = \frac{58}{125}

Answer:

\frac{58}{125}

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