Question

The overall percentage of failure in a certain examination is 0.30. what is the probability that out of a group of 6 candidates at least 4 passed the examination?

(a) 0.5443
(b) 0.4543
(c) 0.5543
(d) 0.4573

Answer 1

To find the probability of at least 4 candidates passing the exam, use the binomial probability formula.

Step-by-step explanation:

To find the probability that at least 4 candidates passed the examination, we can use the binomial probability formula. Let's break it down step-by-step:

1. Define the probability of success (passing the examination) as p = 1 - 0.30 = 0.70.
2. Define the number of trials (number of candidates) as n = 6.
3. Calculate the probability of exactly 4, 5, and 6 candidates passing the exam using the binomial probability formula: P(x=k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the number of combinations of n items taken k at a time.
4. Sum up the probabilities of exactly 4, 5, and 6 candidates passing the exam.
5. Finally, subtract the sum from 1 to find the probability of at least 4 candidates passing the exam.

Using this approach, we find that the probability is approximately 0.5443 (option a).