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)*\mathbb P(Y)`.

So


`\mathbb P(X\cap Y)=\frac13*\frac12=\frac16`

Answer 2

Answer: a.
`(1)/(6)`

Explanation:

Given : Events X and Y are independent.

The probability of X occurring is
`(1)/(3)`.

The probability of Y occurring is
`(1)/(2)`.

Since both events are independent, then we have

`\text{P(X and Y)}=\text{P(X)}* \text{P(Y)}\\\\\Rightarrow\ \text{P(X and Y)}=(1)/(2)*(1)/(3)=(1)/(6)`

Hence,
`\text{P(X and Y)}=(1)/(6)`

Thus , (a.) is the correct option.