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Answer :
Final answer:
The question is about calculating the probability of exactly 21 out of 42 customers being loyalty club members. This is done by using the binomial probability formula with 42 trials, 21 desired successes, and a 0.5 probability of success for each trial.
Explanation:
The student is asking about the probability that exactly 21 out of 42 customers are loyalty club members and 21 are not, given that approximately half of the customers who shop at the grocery are loyalty club members. To calculate this probability, we will use the binomial probability formula:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where:
- n is the number of trials (customers) - in this case, 42.
- x is the number of successes (loyalty club members) we want to find the probability for - in this case, 21.
- p is the probability of success on any given trial - since half of the customers are members, this is 0.5.
- (n choose x) is the binomial coefficient, which is calculated as n! / [x! * (n-x)!].
Applying the values to the formula, we get:
P(21) = (42 choose 21) * (0.5)^21 * (0.5)^(42-21)
After calculating (42 choose 21) and simplifying, we can obtain the exact probability.
Learn more about binomial probability here:
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