4. Suppose that a family has three children, each of which is a boy or a girl, and we assume that boys and girls are equally likely at birth. a. The probability that all three children in the family are boys, if it's known that the oldest child in the family is a boy, is b. The probability that two children in the family are boys, given that at least one child
4. Suppose that a family has three children, each of which is a boy or a girl, and we assume that boys and girls are equally likely at birth. a. The probability that all three children in the family are boys, if it's known that the oldest child in the family is a boy, is b. The probability that two children in the family are boys, given that at least one child
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Solve question #4 and solve part a and part b. Please and thank you

Transcribed Image Text:4.
Suppose that a family has three children, each of which is a boy or a girl, and we assume that
boys and girls are equally likely at birth.
a. The probability that all three children in the family are boys, if it's known that the oldest child
in the family is a boy, is
b. The probability that two children in the family are boys, given that at least one child
in the family is a boy, is
State sample space of random experiment in which three births in the family are observed.
Use b for a boy and g for a girl.
S=
Assuming that the event "Three children in the family are boys " is denoted by A,
the event "The oldest child in the family is a boy" is denoted by B,
the event "Two children in the family are boys" is denoted by C, and
the event "At least one child in the family is a boy" is denoted by D,
show your work in answering the questions a. and b.
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