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.

The probability of getting 6's on both cubes is .

The probability that the total score is at least 11 is .

Step-by-step 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

Probability of getting 6 on blue cube is

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

Hence, the probability of getting 6's on both cubes is .

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.

Hence, the probability that the total score is at least 11 is .

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

answer are

step-by-step explanation: