Two newspapers X and Y are published in a certain city. It is estimated from a survey that16% read X, 14% read Y and 5% read both the newspapers. Find the probability that a randomlyselected person does not read any newspaper.
Question
Two newspapers X and Y are published in a certain city. It is estimated from a survey that16% read X, 14% read Y and 5% read both the newspapers. Find the probability that a randomlyselected person does not read any newspaper.
Solution
To solve this problem, we need to understand that the total probability of all events in a certain space is always 1. In this case, the events are: reading newspaper X, reading newspaper Y, reading both newspapers, and reading no newspapers.
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First, we calculate the probability of reading newspaper X or Y. This is the sum of the individual probabilities minus the probability of the intersection (people who read both newspapers). So, P(X or Y) = P(X) + P(Y) - P(X and Y) = 16% + 14% - 5% = 25%.
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Now, we want to find the probability of the event that a person does not read any newspaper. This is the complement of the event that a person reads newspaper X or Y. So, P(No newspaper) = 1 - P(X or Y) = 1 - 25% = 75%.
Therefore, the probability that a randomly selected person does not read any newspaper is 75%.
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