There are 3 first grade children, 5 second grade children, and 7 third grade children in a room. When choosing two children, what is the conditional probability of choosing a
Second grade child, given that either a first or a third grade child was chosen first?
A) $\frac { 5 } { 7 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 2 } { 7 }$
D) $\frac { 5 } { 14 }$

Question

There are 3 first grade children, 5 second grade children, and 7 third grade children in a room. When choosing two children, what is the conditional probability of choosing a
Second grade child, given that either a first or a third grade child was chosen first? 
A) $\frac { 5 } { 7 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 2 } { 7 }$
D) $\frac { 5 } { 14 }$

Quizplus · Accepted Answer

Given that either a first or third grade child was chosen first, we have 10 children left (3+7=10, excluding second graders initially). The probability of choosing a second grade child next is 5 out of the remaining 14 children (5 second graders + 9 first and third graders), so $\frac{5}{14}$.

There Are 3 First Grade Children, 5 Second Grade Children 57\frac { 5 } { 7 }75​

There Are 3 First Grade Children, 5 Second Grade Children $\frac { 5 } { 7 }$