Question

1. (a) A class has 10 boys and 5 girls. Three students are selected at random one after another. Find the probability that (i) first two are boys and third is girl (ii) first and third are of same sex and the second is of opposite sex.
(b) Two aero planes bomb a target in succession. The probability of each correctly scoring a hit is 0.3 and 0.2 respectively. The second will bomb only if the first misses the target. Find the probability that (i) target is hit (ii) both fails to score hits.

Answer 1

Answer on Question #53299 - Math - Statistics and Probability

(a) A class has 10 boys and 5 girls. Three students are selected at random one after another. Find the probability that

(i) first two are boys and third is girl;

(ii) first and third are of same sex and the second is of opposite sex.

(b) Two aero planes bomb a target in succession. The probability of each correctly scoring a hit is 0.3 and 0.2 respectively. The second will bomb only if the first misses the target. Find the probability that

(i) target is hit;

(ii) both fails to score hits.

Solution

(a)

(i) Probability that first two are boys and third is girl:

$$P(bbg) = \frac{10}{15} \cdot \frac{9}{14} \cdot \frac{5}{13} = \frac{15}{91}$$

(ii) Probability that first and third are of same sex and the second is of opposite sex:

$$P = P(gbg) + P(gbg) = \frac{10}{15} \cdot \frac{5}{14} \cdot \frac{9}{13} + \frac{5}{15} \cdot \frac{10}{14} \cdot \frac{4}{13} = \frac{5}{21}$$

(b)

(i) Probability that target is hit:

$$P(hit) = 0.3 + 0.7 * 0.2 = 0.44$$

(ii) Probability that both fails to score hits:

$$P(both\ miss) = 0.7 * 0.8 = 0.56$$

Answer:

(a)

(i) $\frac{15}{91}$

(ii) $\frac{5}{21}$

(b)

(i) 0.44

(ii) 0.56

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