Question

The Probability of hitting the target by a trained sniper is three times the Probability of not hitting the target on a stormy day due to high wind speed.

The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that

1. target is hit
2. atleast one shot misses the target.

Answer 1

(i) Let P(H) be the probability of hitting the target.

P(M) be the probability of missing the target.

P(H) + P(M) = 1

P(H) = 3 P(M)

P(H) = 3(1 – P(H))

P(H) = 3 – 3P(H)

4P(H) = 3

P(H) = `3/4`

(ii) If both shot hit = P(H)·P(H)

= `3/4*3/4`

= `9/16`

P (at least one shot missing out) = `1-9/16`

= `7/16`