A survey of top executives revealed that 37% of them regularly read Time magazine, 21% read Newsweek and 38% read U.S. News & World Report. Eleven percent read both Time and U.S. News & World Report. What is the probability that a particular top executive reads either Time or U.S. News & World Report regularly?
1.00
0.29
0.49
0.64
To find the probability that a particular top executive reads either Time or U.S. News & World Report regularly, we need to determine the percentage of executives who read either of these magazines.
Given that 37% read Time magazine, 38% read U.S. News & World Report, and 11% read both Time and U.S. News & World Report, we can calculate the probability using the formula:
P(Time or U.S. News & World Report) = P(Time) + P(U.S. News & World Report) - P(Time and U.S. News & World Report)
P(Time or U.S. News & World Report) = 37% + 38% - 11% = 64%
Therefore, the probability that a particular top executive reads either Time or U.S. News & World Report regularly is 0.64, or 64%.
To find the probability that a particular top executive reads either Time or U.S. News & World Report regularly, we need to calculate the union of the probabilities of reading each magazine individually.
First, let's calculate the probability of reading Time or U.S. News & World Report separately.
The probability of reading Time magazine regularly is given as 37%.
The probability of reading U.S. News & World Report regularly is given as 38%.
Now, we need to find the probability of reading both Time and U.S. News & World Report. According to the survey, 11% of the top executives read both magazines.
To find the probability of reading either Time or U.S. News & World Report, we need to add the probabilities of reading each magazine and subtract the probability of reading both magazines to avoid double-counting.
P(Time or U.S. News & World Report) = P(Time) + P(U.S. News & World Report) - P(Time and U.S. News & World Report)
= 37% + 38% - 11%
= 74% - 11%
= 63%
Therefore, the probability that a particular top executive reads either Time or U.S. News & World Report regularly is 0.63 or 63%.
So, the correct answer is 0.64, which is the closest option given in the choices.