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A family has j children with probability pj, where p1= .1,
Chapter 3, Problem 32P(choose chapter or problem)
Problem 32P
A family has j children with probability pj, where p1= .1, p2 = .25, p3 = .35, p4 = .3. A child from this family is randomly chosen. Given that this child is the eldest child in the family, find the conditional probability that the family has
(a) only 1 child;
(b) 4 children.
Redo (a) and (b) when the randomly selected child is the youngest child of the family.
Questions & Answers
QUESTION:
Problem 32P
A family has j children with probability pj, where p1= .1, p2 = .25, p3 = .35, p4 = .3. A child from this family is randomly chosen. Given that this child is the eldest child in the family, find the conditional probability that the family has
(a) only 1 child;
(b) 4 children.
Redo (a) and (b) when the randomly selected child is the youngest child of the family.
ANSWER:
Step 1 of 2
Given a family has j children with probability pj,
We consider = .1,
= .25, p3 = .35,
= .3.
Our goal is :
a). We need to find the probability of only one child.
b). We need to find the probability of 4 children.
Let denotes the events that the Family has 1, 2, 3, and 4 children respectively.
Let E be the evidence that the chosen child is the eldest in the Family.
a). Now we have to compute the probability of only one child.
Then the probability of only one child is
P
We will begin by computing P(E).
We consider and
.
We find the P(E).
P(E) =
P(E)
P(E) = 1(0.1) + (0.25) +
(0.35) +
(0.3)
P(E) = 0.4167
Therefore, the probability of only one child is 0.4167.