The probability that daughters of a mother who attends church regularly will also attend church regularly is 0.9, whereas the probability that daughters of a mother who does not attend regularly will attend regularly is 0.2.
If a woman attends church regularly and has one daughter, who in turn has one daughter, what is the probability that the granddaughter attends church regularly? Round your answer to two decimal places.

A)0.66
B)0.42
C)0.17
D)0.81
E)0.83

Question

The probability that daughters of a mother who attends church regularly will also attend church regularly is 0.9, whereas the probability that daughters of a mother who does not attend regularly will attend regularly is 0.2. ​
If a woman attends church regularly and has one daughter, who in turn has one daughter, what is the probability that the granddaughter attends church regularly? Round your answer to two decimal places.
​
A)0.66
B)0.42
C)0.17
D)0.81
E)0.83

Quizplus · Accepted Answer

According to the problem, the probability that the mother attends church regularly is 1. Therefore, the probability that the daughter of the mother attends church regularly is 0.9. Similarly, the probability that the daughter of a mother who does not attend regularly will attend regularly is 0.2.
Since we know that the mother attends church regularly, there are two possible cases for the granddaughter:
1. The daughter of the mother attends church regularly and the granddaughter of the mother also attends church regularly.
2. The daughter of the mother does not attend church regularly and the granddaughter of the mother attends church regularly.
The probability that the granddaughter attends church regularly can be calculated as:
(Probability that granddaughter attends | daughter attends) * (Probability that daughter attends) + (Probability that granddaughter attends | daughter does not attend) * (Probability that daughter does not attend) 
= (0.9 * 0.9) + (0.2 * 0.1)
= 0.81 + 0.02
= 0.83
Therefore, the probability that the granddaughter attends church regularly is 0.83, which is closest to option E (0.83).

The Probability That Daughters of a Mother Who Attends Church