Question

Example 2: Combining Use of the Multiplication and Addition Rules

A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way. The two cubes are rolled. Find the probability of each event.
a. Both cubes show 6’s.
b. The total score is at least 11.

Answer 1

The probability of getting 6's on both cubes is
`(1)/(36)`.

The probability that the total score is at least 11 is
`(1)/(12)`.

Explanation:

Consider the provided information.

A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way.

Part (A) Both cubes show 6’s.

Probability of getting 6 on red cube is
`(1)/(6)`

Probability of getting 6 on blue cube is
`(1)/(6)`

Thus, the probability of getting 6's on both cubes is:

`P(\text{Both 6's})=(1)/(6)*(1)/(6)=(1)/(36)`

Hence, the probability of getting 6's on both cubes is
`(1)/(36)`.

Part (B) The total score is at least 11.

The possible number of outcomes in which total score is at least 11 is:

Red shows 6 and Blue shows 5.

Blue shows 6 and Red shows 5.

Blue shows 6 and Red shows 6.

Thus, the probability of total score is at least 11.

`P(\text{Total is at least 11})=(1)/(6)*(1)/(6)+(1)/(6)*(1)/(6)+(1)/(6)*(1)/(6)\\P(\text{Total is at least 11})=(1)/(12)`

Hence, the probability that the total score is at least 11 is
`(1)/(12)`.