A class consists of seven boys and 9 girls. Two different members of the class are chosen at random. A is the event {the first person is a girl}, and B is the event {the second person is a girl}. Find the probability of:
a) B|A'
Please Help !
A class consists of seven boys and 9 girls. Two different members of the class are chosen at random. A is the event {the first person is a girl}, and B is the event {the second person is a girl}. Find the probability of:
a) B|A'
Please Help !
$\displaystyle P(B|A)$ is asking us what if the prob a randomly getting a girl is you have already pick one.
This just reduces your sample space. After you have picked the first girl there are now 7 boys and 8 girls to choose from.
To the probability is $\displaystyle P(B|A)=\frac{8}{15}$
after thought: does $\displaystyle B|A'$ mean A compliment i.e $\displaystyle B|A^c$ if that is the case the same reasoning as above would still work exept you would remove a boy instead of a girl from your sample space.
Hello, creatively12!
A class consists of 7 boys and 9 girls.
Two members of the class are chosen at random.
$\displaystyle A$ = (1st person is a girl}, and $\displaystyle B$ = (2nd person is a girl}.
Find: .$\displaystyle (a)\;P(B\,|\,A')$
We want: .$\displaystyle P(B\,|\,A') \;=\;P(\text{2nd is girl}\,|\,\text{1st is a boy})$
Since the first chosen is a boy,
. . there are 6 boys and 9 girls to choose from.
Then the probability of choosing a girl is: .$\displaystyle \tfrac{9}{15} \:=\:\tfrac{3}{5}$
Therefore: .$\displaystyle P(\text{2nd is girl}\,|\,\text{1st is boy}) \;=\;\frac{3}{5}$