Ronald and Michelle have two children. The probability that the first child is a girl is 50%. The probability that the second child is a girl is also 50%. Ronald and Michelle tell you that they have a daughter. The Question: What is the probability that their other child is also a girl?

  1. 33%

  2. 66%

  3. 50%

  4. 100%


Correct Option: A

AI Explanation

To answer this question, we can use the concept of conditional probability. The probability of an event A occurring given that event B has already occurred is denoted as P(A|B).

In this case, we are given that Ronald and Michelle have two children, and the probability that the first child is a girl is 50%. Let's denote this event as A. The probability that the second child is a girl is also 50%, denoted as event B.

We are also told that Ronald and Michelle have a daughter. Let's denote this event as C. We want to find the probability that their other child is also a girl, which is the probability of event A occurring given that event C has occurred, or P(A|C).

To calculate P(A|C), we can use Bayes' theorem:

P(A|C) = (P(C|A) * P(A)) / P(C)

P(C|A) is the probability of having a daughter given that the first child is a girl, which is 1 (since we are given that they have a daughter). P(A) is the probability of the first child being a girl, which is 0.5. P(C) is the probability of having a daughter, which can be calculated by considering the two possible combinations of genders for the two children: boy-girl and girl-girl. Since we are given that they have a daughter, the probability of having a daughter is 2/3 (boy-girl and girl-girl are possible combinations, and only one of them results in a daughter).

Plugging the values into Bayes' theorem:

P(A|C) = (1 * 0.5) / (2/3) P(A|C) = 0.5 / (2/3) P(A|C) = 0.5 * (3/2) P(A|C) = 0.75

Therefore, the probability that their other child is also a girl is 0.75, which is equivalent to 75%. Thus, the correct answer is not listed among the given options.

In conclusion, the answer provided in the question is incorrect.

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