+0

0
200
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There are 7 students in a class: 2 boys and 5 girls. If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?

Jun 4, 2021

#1
+2322
+2

5/7 * 4/6 * 3/5.

At first person she picks has 5/7 chance of being a girl, then 4/6, then 3/5.

=^._.^=

Jun 4, 2021
#2
+26228
+4

There are 7 students in a class: 2 boys and 5 girls.
If the teacher picks a group of 3 at random,
what is the probability that everyone in the group is a girl?

$$\begin{array}{|rcll|} \hline \dfrac{ \binom{2}{0}_{\text{Boys}}\binom{5}{3}_{\text{Girls} } } {\binom{7}{3}_{\text{Boys and Girls} } } &=& \dfrac{2}{7}\\ \text{or} \\ \dfrac{5}{7}*\dfrac{4}{6}*\dfrac{3}{5}&=& \dfrac{2}{7}\\ \hline \end{array}$$

The probability is $$\approx 28.57 \%$$

Jun 4, 2021