Exercise 34 Page 799

We want to know the probability of randomly selecting a red or blue marble from a bag. These events are mutually exclusive, as we cannot select a red and blue marble. Let's recall the formula for the probability of mutually exclusive events

A

and

B .

P (A or B) = P (A) + P (B)

We can see that George multiplied instead of adding, so his solution is incorrect. Let's see if Aliyah added correctly. We are told that there are

8

blue marbles,

6

red marbles,

8

yellow marbles, and

4

white marbles in the bag. By adding these numbers together we can find the total marbles in the bag.

8 + 6 + 8 + 4 = 26

To find the probability that we select a blue marble, we will divide the number of blue marbles by the total amount of marbles.

P (blue) = \frac{8}{2 6}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

P (blue) = \frac{4}{1 3}

Similarly, we will divide the amount of red marbles by the total amount of marbles to find the probability of selecting a red marble.

P (red) = \frac{6}{2 6}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

P (red) = \frac{3}{1 3}

Let

A

be the probability of choosing a red marble and

B

the probability of choosing a blue marble. Let's substitute our values into the formula for mutually exclusive events.

P (blue or red) = P (blue) + P (red)

SubstituteValues

Substitute values

P (blue or red) = \frac{4}{1 3} + \frac{3}{1 3}

AddFrac

Add fractions

P (blue or red) = \frac{7}{1 3}

Let's write this probability as a percent.

P (blue or red) = \frac{7}{1 3}

CalcQuot

Calculate quotient

P (blue or red) = 0.538461 \dots

RoundDec

Round to $2$ decimal place(s)

P (blue or red) \approx 0.54

WritePercent

Convert to percent

P (blue or red) \approx 54 %

We can see that Aliyah is correct.