A gardener plants 8 seeds, and each has a 65% probability of germinating successfully. Find the probability that less than 4 seeds germinate successfully.

• A. 0.0266
• B. 0.0252
• C. 0.1062
• D. 0.0084

Answer: (C)

Verified step by step guidance

1. Identify the type of probability distribution involved. Since each seed has a fixed probability of germinating, and the outcome is either germination or not, this is a binomial distribution problem.
2. Define the parameters of the binomial distribution: n = 8 (number of trials, i.e., seeds), p = 0.65 (probability of success, i.e., germination).
3. To find the probability that less than 4 seeds germinate, calculate the cumulative probability for 0, 1, 2, and 3 seeds germinating. This involves summing the probabilities of these individual events.
4. Use the binomial probability formula for each case: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the binomial coefficient, n is the number of trials, k is the number of successes, p is the probability of success, and (1-p) is the probability of failure.
5. Calculate the cumulative probability: P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Sum these probabilities to find the total probability that less than 4 seeds germinate.