Among 38-43 year old, 25% say they have written an editorial letter while under the influence of peer pressure. Suppose two 38-43 year old are selected at random. (a )what is the probability that at least one has not written under the influence of peer pressure. (b) what is the probability of that at least one has written an editorial letter while under the influence of peer pressure
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To solve this problem, we can use probability calculations based on the given information.
(a) To find the probability that at least one person has not written an editorial letter under the influence of peer pressure, we can use the complement rule. The complement of at least one person not writing is that both have written. So, we can calculate the probability of both writing under peer pressure and then subtract it from 1.
Given that 25% of 38-43-year-olds have written under peer pressure, the probability of one person writing under peer pressure is 0.25. Therefore, the probability of both writing under peer pressure is 0.25 * 0.25 = 0.0625.
Now, we can calculate the probability of at least one person not writing under peer pressure:
P(at least one has not written under peer pressure) = 1 - P(both writing under peer pressure)
= 1 - 0.0625
= 0.9375
Therefore, the probability that at least one person has not written an editorial letter under the influence of peer pressure is 0.9375, or 93.75%.
(b) Similarly, to find the probability that at least one person has written an editorial letter under the influence of peer pressure, we can calculate the complement of both not writing under peer pressure.
Given that 25% of 38-43-year-olds have written under peer pressure, the probability of one person writing is 0.25. Thus, the probability of both not writing under peer pressure is 0.75 * 0.75 = 0.5625.
Now, we can calculate the probability of at least one person writing under peer pressure:
P(at least one has written under peer pressure) = 1 - P(both not writing under peer pressure)
= 1 - 0.5625
= 0.4375
Therefore, the probability that at least one person has written an editorial letter under the influence of peer pressure is 0.4375, or 43.75%.