Question

A patient going in to a doctor’s waiting room reads Hiya Magazine with probability 0.6 and Dakor Magazine with probability 0.4. The probability that the patient reads either one or both of the magazines is 0.7. Find the probability that the patient reads a both magazines, b Hiya Magazine only.

Answer 1

The probability that the patient reads both magazines is 0.3, and the probability of reading Hiya Magazine only is also 0.3.

Step-by-step explanation:

The question involves calculating probabilities of combined events using the addition rule in probability theory. The patient's probabilities for reading magazines are given as 0.6 for Hiya Magazine and 0.4 for Dakor Magazine with the additional information that the probability of reading either one or both is 0.7.

1. First, find the probability that the patient reads both magazines by using the formula for the probability of the union of two events: P(A OR B) = P(A) + P(B) - P(A AND B). This formula allows us to rearrange and solve for P(A AND B).
2. To find the probability that the patient reads Hiya Magazine only, subtract the probability of reading both magazines from the probability of reading Hiya.

We can perform these calculations step by step:

1. 0.7 = 0.6 + 0.4 - P(A AND B), so P(A AND B) = 0.6 + 0.4 - 0.7 which equals 0.3.
2. P(Hiya only) = P(Hiya) - P(A AND B) = 0.6 - 0.3 which equals 0.3.