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A public library carries 50 magazines, each of which focuses on either news or sports. Thirty of the magazines focus on news, and the remaining 20 focus on sports. Among the 30 news magazines, 20 include international news, and 10 include national news only. Among the 20 sports magazines, 5 focus on international sports, and the remaining 15 focus on national sports only.

A customer randomly picks a magazine from the shelf and notices that it is a news magazine. Given that it is a news magazine, what is the probability that it includes international news?

Answer :

Final answer:

The probability that a randomly picked news magazine from the library includes international news is 2/3 or approximately 66.7%.

Explanation:

The question pertains to the concept of conditional probability in mathematics. The problem tells us that there are 30 news magazines, out of which 20 include international news and 10 include only national news.

The customer has already picked out a news magazine, so we are only considering the subset of magazines that are categorized as news. We want to find the probability that among these news magazines, the one picked includes international news.

To calculate this, we use the formula for conditional probability, which is:

Probability(B given A) = Probability(A and B) / Probability(A), where
"A" represents picking a news magazine, and
"B" represents picking a magazine that includes international news.

Since the question has already given that a news magazine is selected, the probability of A is 1. Therefore, the calculation simplifies to the probability of B:

Probability that the selected magazine includes international news given it's a news magazine = Number of international news magazines / Total number of news magazines = 20 / 30 = 2/3 or approximately 0.667, which translates to a 66.7% chance.

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Rewritten by : Barada