Exercise 15 Page 848

We select a chip randomly from a bag that contains 3 blue chips, 6 black chips, 2 green chips, and 4 red chips. We are asked to find the probability that we select a green chip or a black chip. Note that we cannot choose a green chip and a black chip at the same time. Therefore, these events are mutually exclusive. If events A and B are mutually exclusive, then the probability that either A or B occurs is the sum of the probability of A occurring and the probability of B occurring. P( Aor B)=P( A)+ P( B)

In order to find the desired probability, we will find the probability that we select a green chip and the probability that we select a black chip one at a time. Let's start by calculating the probability of choosing a green chip.

Out of 15 chips in the bag, there are 2 green chips. P( green chip)= 2/15 Next, we will calculate the probability of choosing a black chip.

Out of 15 chips in the bag, there are 6 black chips. P( black chip)= 6/15=2/5 Finally, we can find the desired probability by adding the obtained probabilities.

P(green chip or black chip)

Substitute

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

P(green chip)+ P(black chip)

SubstituteII

P(green chip)= 2/15, P(black chip)= 2/5

2/15+ 2/5

ExpandFrac

a/b=a * 3/b * 3

2/15+6/15

AddFrac

Add fractions

8/15

Therefore, the probability P(green chip or black chip) is equal to 815.