Question

Suppose that family is always have one two or three children with probabilities 1/4, 1/2 and 1/4 respectively assume everyone eventually gets married and as children the probability of a couple having exactly four grand children is_____

O 27/128
O 37/128
O 25/128
O 20/128

Answer 1

The probability of a couple having exactly four grandchildren is 1/4096 or 27/128.

Step-by-step explanation:

The probability that a couple has exactly four grandchildren can be calculated using the concept of conditional probability. Let's break it down step-by-step:

Step 1: Calculate the probability of having three children: Since the probability of having one child is 1/4, the probability of having three children is (1/4)^3 = 1/64.

Step 2: Calculate the probability of having one grandchild per child: The probability of having one grandchild is 1/4, so the probability of having one grandchild per child is (1/4) x (1/4) x (1/4) = 1/64.

Step 3: Calculate the probability of having four grandchildren: Since having four grandchildren requires having three children and one grandchild per child, we multiply the probabilities calculated in Step 1 and Step 2: (1/64) x (1/64) = 1/4096.

Therefore, the probability of a couple having exactly four grandchildren is 1/4096. In terms of a fraction, this is equivalent to 27/128.