Question

An executive committee consists of 13 members: 7 men and 6 women. 3 members are selected at random to attend a meeting in Hawaii. The names are drawnfrom a hat. What is the probability that all 3 selected are women?

Answer 1

10/143

Explanations:

Probability is the likelihood or chance that an event will occur.

If an executive committee consists of 13 members: 7 men and 6 women and 3 members are selected at random, the total outcome will be expressed according to the combination rule:

`\begin{gathered} 13C_3=(13!)/((13-3)!3!) \\ 13C_3=(13!)/(10!3!) \\ 13C_3=(13*12*11*10!)/(10!*6) \\ 13C_3=13*22=286 \end{gathered}`

If all the selected executive are women, then the expected outcome will be:

`\begin{gathered} 7C_0*6C_3=(7!)/((7-0)0!)*(6!)/((6-3)!3!) \\ 7C_0*6C_3=(7!)/(7!0!)*(6!)/(3!3!) \\ 7C_0*6C_3=(1)/(0!)*(6*5*4*6)/(6*6) \\ 7C_0*6C_3=20 \end{gathered}`

The probability that all 3 selected are women will be:

`\begin{gathered} Pr(all\text{ selected are women})=(7C_0*6C_3)/(8C_3) \\ Pr(all\text{ selected are women})=(20)/(286) \\ Pr(all\text{ selected are women})=(10)/(143) \end{gathered}`

Therefore the probability that all 3 selected are women is 10/143