Question

Events X and Y are independent. The probability of X occurring is 1/3 . The probability of Y occurring is 1/2 . What is P(X and Y)?
a. 1/6
b. 1/3
c.2/3
d.5/6

Answer 1

For independent events $X,Y$, $\mathbb P(X\cap Y)=\mathbb P(X)\times\mathbb P(Y)$.

So

$\mathbb P(X\cap Y)=\dfrac13\times\dfrac12=\dfrac16$

Answer 2

Answer: a. $\dfrac{1}{6}$

Step-by-step explanation:

Given : Events X and Y are independent.

The probability of X occurring is $\dfrac{1}{3}$.

The probability of Y occurring is $\dfrac{1}{2}$.

Since both events are independent, then we have

$\text{P(X and Y)}=\text{P(X)}\times \text{P(Y)}\\\\\Rightarrow\ \text{P(X and Y)}=\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}$

Hence, $\text{P(X and Y)}=\dfrac{1}{6}$

Thus , (a.) is the correct option.