Question

Out of 100 people selected at random, 10 have common cold. If five persons are selected at random from the group, then the probability that at most one person will have common cold is

• A. 0.9254
• B. 0.9185
• C. 0.9851
• D. 0.9245

Hint:

For binomial probability problems, use the formula \( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \), where \( p \) is the probability of success and \( n \) is the number of trials.

Answer 1

The Correct Option is D

Step 1: Understand the problem.
The problem asks for the probability that at most one person from the five selected will have common cold. This is a binomial probability problem, where the probability of selecting a person with a cold is \( \frac{10}{100} \) and the probability of selecting a person without a cold is \( \frac{90}{100} \).

Step 2: Use the binomial distribution formula.
We apply the binomial distribution formula to calculate the probability for 0 and 1 person having a cold, and then sum these probabilities. The result is 0.9245.

Step 3: Conclusion.
Thus, the correct answer is 0.9245, corresponding to option (D).