probability that everyone in the group is a boy = 0.1428
Step-by-step explanation:
Here we have , There are 7 students in a class: 5 boys and 2 girls. If the teacher picks a group of 4 at random, We need to find what is the probability that everyone in the group is a boy . Let's find out:
Initially we have , 7 students out of which 5 boys, so probability choosing first boy will be :
⇒ [tex]\frac{5}{7}[/tex]
After this we are left with 6 students and 4 boys , so probability choosing second boy :
⇒ [tex]\frac{4}{6}[/tex]
After this we are left with 5 students and 3 boys , so probability choosing third boy :
⇒ [tex]\frac{3}{5}[/tex]
After this we are left with 4 students and 2 boys , so probability choosing fourth boy :
⇒ [tex]\frac{2}{4}[/tex]
So, probability that everyone in the group is a boy = [tex]\frac{5}{7} (\frac{4}{6} ) (\frac{3}{5} ) (\frac{2}{4} )[/tex] = [tex]\frac {1} {7}[/tex]
probability that everyone in the group is a boy = 0.1428
