Question

Ethan counted the boxes of cereal in a grocery store with different sizes and numbers of prizes The probability that a box of cereal is mini size is 0.6, the probability that it contains two prizes is 0.3, and the probability that it is mini size or contains two prizes is 0.7.What is the probability that a randomly chosen box of cereal is mini size and contains two prizes?

A) 0.1
B) 0.2
C) 0.3
D) 0.4

Answer 1

The probability that a randomly chosen box of cereal is mini-sized and contains two prizes is calculated using a formula involving the individual probabilities and their union, yielding a probability of 0.2.

Step-by-step explanation:

The question asks for the probability that a randomly chosen box of cereal is a mini size and contains two prizes. To find this, we can use the formula P(A and B) = P(A) + P(B) - P(A or B), where P(A) is the probability of event A, P(B) is the probability of event B, and P(A or B) is the probability of either event A or event B occurring.

Given that P(mini size) = 0.6, P(two prizes) = 0.3, and P(mini size or two prizes) = 0.7, we can substitute these into our formula:

P(mini size and two prizes) = P(mini size) + P(two prizes) - P(mini size or two prizes)

P(mini size and two prizes) = 0.6 + 0.3 - 0.7

P(mini size and two prizes) = 0.2

Therefore, the correct answer is B) 0.2.