Consider a political discussion group consisting of 4 Democrats, 6 Republicans, and 5 Independents. Supposethat two group members are randomly selected, in succession, to attend a political convention. Find theprobability of selecting an Independent and then a Republican.
A) $\frac { 1 } { 7 }$
B) $\frac { 2 } { 15 }$
C) $\frac { 2 } { 105 }$
D) $\frac { 1 } { 42 }$

Question

Consider a political discussion group consisting of 4 Democrats, 6 Republicans, and 5 Independents. Supposethat two group members are randomly selected, in succession, to attend a political convention. Find theprobability of selecting an Independent and then a Republican. 
A) $\frac { 1 } { 7 }$
B) $\frac { 2 } { 15 }$
C) $\frac { 2 } { 105 }$
D) $\frac { 1 } { 42 }$

Quizplus · Accepted Answer

The probability of selecting an Independent first is $ \frac{5}{15} $. After selecting an Independent, there are 14 people left, with 6 being Republicans. The probability of then selecting a Republican is $ \frac{6}{14} $. Thus, the combined probability is $ \frac{5}{15} \times \frac{6}{14} = \frac{1}{7} $.

Consider a Political Discussion Group Consisting of 4 Democrats, 6 17\frac { 1 } { 7 }71​

Consider a Political Discussion Group Consisting of 4 Democrats, 6 $\frac { 1 } { 7 }$