Find the indicated probability.
-A committee of three people is to be formed. The three people will be selected from a list of five possible committeemembers. A simple random sample of three people is taken, without replacement, from the group of five people. If thefive people are represented by the letters A, B, C, D, E, the possible outcomes are as follows.
$\begin{array}{l}
\mathrm{ABC} \
\mathrm{ABD} \
\mathrm{ABE} \
\mathrm{ACD} \
\mathrm{ACE} \
\mathrm{ADE} \
\mathrm{BCD} \
\mathrm{BCE} \
\mathrm{BDE}
\end{array}$

Determine the probability that B and C are both included in the sample.
A) $\frac { 3 } { 10 }$

B) $\frac { 1 } { 10 }$

C) $\frac { 9 } { 10 }$

D) $\frac { 2 } { 10 }$

Question

Find the indicated probability.
-A committee of three people is to be formed. The three people will be selected from a list of five possible committeemembers. A simple random sample of three people is taken, without replacement, from the group of five people. If thefive people are represented by the letters A, B, C, D, E, the possible outcomes are as follows. 
$\begin{array}{l}
\mathrm{ABC} \
\mathrm{ABD} \
\mathrm{ABE} \
\mathrm{ACD} \
\mathrm{ACE} \
\mathrm{ADE} \
\mathrm{BCD} \
\mathrm{BCE} \
\mathrm{BDE}
\end{array}$

Determine the probability that B and C are both included in the sample. 
A) $\frac { 3 } { 10 }$

B) $\frac { 1 } { 10 }$

C) $\frac { 9 } { 10 }$

D) $\frac { 2 } { 10 }$

Quizplus · Accepted Answer

The probability that B and C are both included in the sample is calculated by counting the number of outcomes that include both B and C and dividing by the total number of outcomes. There are 3 outcomes (BCD, BCE, BDE) that include both B and C out of a total of 10 possible outcomes, so the probability is $\frac{3}{10}$.

Find the Indicated Probability Determine the Probability That B and C Are Both Included