Final answer:
The probability that exactly 2 out of 4 copiers will break down on a given day is calculated using the binomial probability formula. After applying the formula, the probability is found to be 0.3456, which corresponds to option (d). The correct answer is option d.
Step-by-step explanation:
The question asks for the probability of exactly 2 out of 4 copiers breaking down on a given day, with the probability of any one copier breaking down being 2/5. This can be discussed as a binomial probability problem, where each copier represents a binomial trial with two possible outcomes: it either breaks down ('success') or it does not ('failure'). The probability of 'success' (copier breaking down) is given as 2/5, and 'failure' is therefore 1 - 2/5 = 3/5.
To calculate the probability of exactly 2 out of 4 copiers breaking down, we use the binomial probability formula:
P(X = k) = (n choose k) * p^k * q^(n-k)
where:
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- n is the total number of trials (copiers), which is 4.
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- k is the number of successes (copiers that break down), which is 2.
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- p is the probability of success, which is 2/5.
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- q is the probability of failure, which is 3/5.
Using the formula, we get:
P(X = 2) = (4 choose 2) * (2/5)^2 * (3/5)^(4-2)
= 6 * (4/25) * (9/25)
= 6 * (36/625)
= 216/625
= 0.3456
Therefore, the correct option is (d) 0.3456.