Question

The probability that a bomb will miss the target is 0.2. Then the probability that out of 10 bombs dropped exactly 2 will hit the target is

• A. \( \frac{288}{5^{10}} \)
• B. \( \frac{144}{5^9} \)
• C. \( \frac{144}{5^{10}} \)
• D. \( \frac{288}{5^9} \)

Hint:

Use the binomial probability formula to calculate the probability of a specific number of successes in a fixed number of trials.

Answer 1

The Correct Option is B

Step 1: Using the binomial probability formula.
The problem involves binomial distribution, where the probability of success (hitting the target) is \( 0.8 \) and the probability of failure (missing the target) is \( 0.2 \). The binomial probability formula is: \[ P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \] where \( n = 10 \), \( k = 2 \), and \( p = 0.8 \).

Step 2: Calculating the probability.
We substitute the values into the binomial formula: \[ P(X = 2) = \binom{10}{2} (0.8)^2 (0.2)^8 \] After simplifying, we find that the probability is \( \frac{144}{5^9} \), which makes option (B) the correct answer.