The random variable X, representing the number of items sold in a week, has the following probability distribution:x 0 1 2 3 4 5 6P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05What is the probability that in a given week there will be at most 4 items sold?
Question
The random variable X, representing the number of items sold in a week, has the following probability distribution:x 0 1 2 3 4 5 6P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05What is the probability that in a given week there will be at most 4 items sold?
Solution
The probability that at most 4 items will be sold in a given week is the sum of the probabilities of selling 0, 1, 2, 3, and 4 items.
From the given probability distribution:
P(X = 0) = 0.10 P(X = 1) = 0.20 P(X = 2) = 0.40 P(X = 3) = 0.15 P(X = 4) = 0.05
So, the probability that at most 4 items will be sold is:
P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= 0.10 + 0.20 + 0.40 + 0.15 + 0.05
= 0.90 or 90%
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