You can use the binomial probability formula ncx this case
Solved Step by Step With Explanation- Binomial Probability Questions Clarification
Questions
Given:
The probability mass function (pmf) of a random variable X, which follows a binomial distribution with parameters n and p, is given by: P(X = x) = nCx * px * q^(n-x), where nCx represents combinations, p is the probability of success, and q is the probability of failure.
nCx is calculated as:
nCx = n! / [x!(n-x)!]
So, the probability that exactly three of these patients suffer from side-effects of the anaesthetic is indeed 0.115. Therefore, option C is correct.
Now, let's calculate the probability that at least two of these patients suffer from side-effects of the anesthetic (P(X ≥ 2)). To do this, we need to find the complementary probability of "none or one patient suffering from side-effects" and then subtract it from 1.
P(X = 1):
nC1 = 7! / [1!(7-1)!] = 7
The provided solution is correct, and options C and D are the correct answers for the respective questions.