The names of eight boys and six girls from your class are put into a hat what is the probability that the first two names chosen will both be boys?

Question

5614 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-31T22:53:39

$\frac{4}{13}$ $4/13$

$Assumption: Selection without replacement.$ $color(blue)("Assumption: Selection without replacement."$

Let the probability of the first selection be $P_{1}$ $P_1$
Let the probability of the second selection be $P_{2}$ $P_2$

$At first selection from the hat there are:$ $color(brown)("At first selection from the hat there are:")$

8 boys + 6 girls $\to$ $->$ Total of 14

So $P_{1} = \frac{8}{14}$ $P_1= 8/14$

$Under the assumption that a boy was selected we now have:$ $color(brown)("Under the assumption that a boy was selected we now have:")$

7 boys + 6 girls $\to$ $->$ Total of 13

So $P_{2} = \frac{7}{13}$ $P_2= 7/13$

$Thus P_{1} and P_{2} = \frac{8}{14} \times \frac{7}{13} = \frac{4}{13}$ $color(blue)("Thus "P_1 " and " P_2 = 8/14xx7/13 = 4/13$