Mr. A can hit a target 4 times with 5 shots. Mr. B can hit it 3 times with 4 shots and Mr. C can hit it 3 times with 5 shots. Each fire a volley, what is the probability that

i. only two shots hit the target?

ii, only one shot hit the target?

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muzammilbhutia3 muzammilbhutia3 · Answer 1 · 2024-03-09T17:39:33+01:00

Answer:

To solve this, let's break down the probabilities for each shooter:

i. To find the probability that only two shots hit the target:

For Mr. A: Probability of hitting 2 shots out of 5.

For Mr. B: Probability of hitting 2 shots out of 4.

For Mr. C: Probability of hitting 2 shots out of 5.

ii. To find the probability that only one shot hits the target:

For Mr. A: Probability of hitting 1 shot out of 5.

For Mr. B: Probability of hitting 1 shot out of 4.

For Mr. C: Probability of hitting 1 shot out of 5.

Let's calculate each:

i. Probability of only two shots hitting the target:

For Mr. A: \( \frac{{\binom{5}{2}}}{{5^2}} \)

For Mr. B: \( \frac{{\binom{4}{2}}}{{4^2}} \)

For Mr. C: \( \frac{{\binom{5}{2}}}{{5^2}} \)

Now, sum up the individual probabilities for each shooter to get the total probability for i.

ii. Probability of only one shot hitting the target:

For Mr. A: \( \frac{{\binom{5}{1}}}{{5^1}} \)

For Mr. B: \( \frac{{\binom{4}{1}}}{{4^1}} \)

For Mr. C: \( \frac{{\binom{5}{1}}}{{5^1}} \)

Again, sum up the individual probabilities for each shooter to get the total probability for ii.