Question

If the probability of wearing a dress is 0.6 and the probability of wearing a tie is 0.3, what is the probability of wearing a tie given that a dress is worn, assuming a conditional probability of 0.625?

a) 0.375
b) 0.500
c) 0.625
d) 0.750

Answer 1

The correct answer to the question is c) 0.625, as it represents the given conditional probability of wearing a tie given that a dress is worn, based on the provided probabilities.

Step-by-step explanation:

The student asks about the probability of wearing a tie given that a dress is worn. This is a question of conditional probability. The probability of wearing a tie, given that a dress is worn, can be calculated using the formula for conditional probability: P(Tie | Dress) = P(Tie and Dress) / P(Dress).

In this situation, we are told the conditional probability P(Tie | Dress) is 0.625. Thus, we are given:
P(Dress) = 0.6 (probability of wearing a dress),
P(Tie | Dress) = 0.625 (conditional probability of wearing a tie given that a dress is worn).

To find P(Tie and Dress), we simply multiply P(Tie | Dress) by P(Dress):
P(Tie and Dress) = P(Tie | Dress) x P(Dress) = 0.625 x 0.6 = 0.375

This value represents the joint probability of both wearing a tie and a dress. The conditional probability P(Tie | Dress) is what we were originally asked for, and since it is given as 0.625, the correct answer is c) 0.625.