Question

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

Answer 1

Answer:

The correct answer option is B. 1/3.

Step-by-step explanation:

We are given that P (A ∩ B') = 2/9 and P (B') = 1/3 and we are to find P (A | B').

We also know that the formula of conditional probability is given by:

P (A | B') = P (A ∩ B') / P (B)

So substituting the given values in the formula above to get the value of P (A | B'):

P (A | B') = $\frac { \frac { 2 } { 9 } } { \frac { 1 } { 3 } } = \frac { 2 } { 9 } \times \frac { 3 } { 1 }$ = 1/3

Answer 2

Answer:

Option B

$P(A|B') = \frac{1}{3}$

Step-by-step explanation:

If B 'is the complement of B then $P(B') = P({\displaystyle {\overline {B}}})=1-P(B) = \frac{2}{3}$

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 $P(A\ and\ B) = \frac{2}{9}$ and $P(B') = \frac{2}{3}$

$P(A|B') = \frac{\frac{2}{9}}{\frac{2}{3}}\\\\P(A|B') = \frac{1}{3}$