Question

according to the general equation for conditional probability if P(AnB)=5/7 and P(B)=7/8 what is P(A|B)

Answer 1

Answer:

$P(A|B)=\frac{40}{49}$

Step-by-step explanation:

We know that

the general equation for conditional probability is

$P(A|B)=\frac{P(AnB)}{P(B)}$

we are given

$P(AnB)=\frac{5}{7}$

$P(B)=\frac{7}{8}$

now, we can plug values

$P(A|B)=\frac{\frac{5}{7}}{\frac{7}{8}}$

now, we can simplify it

$P(A|B)=\frac{5\cdot \:8}{7\cdot \:7}$

so, we get

$P(A|B)=\frac{40}{49}$

Answer 2

Answer:

$\frac{40}{49}$

Step-by-step explanation:

We are given the probabilities P(A∩B)=5/7 and P(B)=7/8 and we are to find P(A|B) according to the general equation for conditional probability.

So we will use the following formula for this:

P(A|B) = P(A∩B) / P(B)

Substituting the given values in the above formula to get:

P(A|B) = $\frac{\frac{5}{7} }{\frac{7}{8} }$ = $\frac{5}{7} * \frac{8}{7}$

P(A|B) = $\frac{40}{49}$