Two dice each numbered from 1 and 6 are thrown together. Let A and B be two events given by
A: even number on the first die.
B: number on the second die is greater than 4.
What is `P(A cap B)` equal to?

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `(2)/(3)`
D. `(1)/(6)`

Answer

C

Explanation

In A there are 18 events possible.
`therefore P(A)=(18)/(36)=(1)/(2)`
In B there are 12 events are possible
`therefore P(B)=(12)/(36)=(1)/(3)`
If `A cap B` there are 6 events are possible
Now, `P(A cup B)=P(A)+P(B)-P(A cap B)` `=(1)/(2)+(1)/(3)+(1)/(6)=(3+2-1)/(6)=(4)/(6)=(2)/(3)`