3 3 - 4 0 Intersection of Events These exercises involve the probability of the intersection of events.

A die is rolled twice. What is the probability of getting a “one” on the first roll and an even number on the second roll?

To find:

The probability of getting a “one” on the first roll and an even number on the second roll.

Given:

A die is rolled twice.

Approach:

The probability of an event E is given as,

P(E)=n(E)n(S)

If E and F are independent events in a sample space S, then the probability of E and F is

P(E∩F)=P(E)P(F) … (1)

Calculation:

A die is rolled twice. Let E be the event of “getting one on the first roll” and F be the event of “getting an even number on the second roll.” So,

E={1}F={2,4,6}n(E)=1n(F)=3

Here, E and F are independent events.

If S is the event that a die is rolled then,