Maureen counted the boxes of cereal in a grocery store with different sizes and numbers of prizes.The probability that a box of cereal is family size is 0.5, the probability that it contains a prize is 0.3, and the probability that it is family size or contains a prize is 0.6.What is the probability that a randomly chosen box of cereal is family size and contains a prize?Write your answer as a whole number, decimal, or simplified fraction.
Question
Maureen counted the boxes of cereal in a grocery store with different sizes and numbers of prizes.The probability that a box of cereal is family size is 0.5, the probability that it contains a prize is 0.3, and the probability that it is family size or contains a prize is 0.6.What is the probability that a randomly chosen box of cereal is family size and contains a prize?Write your answer as a whole number, decimal, or simplified fraction.
Solution
To find the probability that a randomly chosen box of cereal is family size and contains a prize, we can use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
We know that:
P(Family Size) = 0.5 P(Prize) = 0.3 P(Family Size or Prize) = 0.6
We can substitute these values into the formula to find the probability that a box is both family size and contains a prize:
0.6 = 0.5 + 0.3 - P(Family Size and Prize)
Solving for P(Family Size and Prize), we get:
P(Family Size and Prize) = 0.5 + 0.3 - 0.6 = 0.2
So, the probability that a randomly chosen box of cereal is family size and contains a prize is 0.2, or 20%.
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