Question

According to the general equation for conditional probability, if (image attached)

A. $\frac{40}{49}$
B. $\frac{24}{49}$
C. $\frac{32}{49}$
D. $\frac{16}{49}$

Answer 1

Answer: Option A

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

Step-by-step explanation:

In a probabilistic experiment, when two events A and B are dependent on each other, then the probability of occurrence A since B occurs is:

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

Then if $P(A\ and\ B) = \frac{5}{7}$ and $P(B) = \frac{7}{8}$ then:

$P(A|B) = \frac{\frac{5}{7}}{\frac{7}{8}}\\\\P(A|B) = \frac{40}{49}$

Answer 2

Answer:

Correct choice is A. $P(A|B)=\frac{40}{49}$.

Step-by-step explanation:

Given that $P(A\cap B)=\frac{5}{7}$, $P(B)=\frac{7}{8}$.

Now using those values , we need to find the value of $P(A|B)$.

So apply the formula of conditional probability:

$P(A\cap B)=P(B) \times P(A|B)$

Plug the given values into above formula,  we get:

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

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

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

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

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

Hence correct choice is A. $P(A|B)=\frac{40}{49}$.