Suppose that a marketing firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that both questionnaires will be returned?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To find the probability that both questionnaires will be returned, we can use the multiplication rule for independent events.
Let's denote the event of a questionnaire being returned by "R" and the event of a questionnaire not being returned by "NR".
We are given that the probability of a questionnaire being returned by each company is 0.30. So, the probability of one questionnaire being returned by a company is 0.30 (R) and the probability of not being returned is 0.70 (NR).
Since the events are independent, we can multiply the probabilities:
P(both questionnaires returned) = P(R Company 1) * P(R Company 2)
= 0.30 * 0.30
= 0.09
Therefore, the probability that both questionnaires will be returned is 0.09 or 9%.
To find the probability that both questionnaires will be returned, we can use the concept of independent events. The probability of two independent events occurring simultaneously is equal to the product of their individual probabilities.
In this case, the probability of one company returning the questionnaire is 0.30. Since the two companies are independent of each other, we can calculate the probability of both questionnaires being returned by multiplying the probabilities together:
P(Both questionnaires returned) = P(Company A returns) * P(Company B returns)
= 0.30 * 0.30
= 0.09
Therefore, the probability that both questionnaires will be returned is 0.09, or 9%.