Question

Suppose you have a bag with 18 small colored stones. There are 6 red stones, 7 green stones, and the rest of the stones  are blue.

a. Would reaching into the bag, pulling out a stone, and recording the color be considered a random experiment? Explain your answer.

b. If you reach into the bag and pull out a stone, what is the probability that the stone is blue?

c. What is the probability that you will not pull out a blue stone?

d. Suppose you pull out a red stone. If you do not replace the first stone, what is the probability that you will pull out a blue stone this time?

Answer 1

(a)

Reaching into the bag, pulling out a stone, and recording the color would be considered a random experiment because in this experiment, the outcome event: the color depends on chance.

(b)

Red stone = 6

Green stone = 7

Blue stone = 5

Total stones = 18

Total number of events = 18

Number of favorable events = 5 (Blue stones)

So,

If you reach into the bag and pull out a stone, what is the probability that the stone is blue = 5/18 = 0.2778

So,

Answer is:

0.2778

(c)

the probability that you will not pull out a blue stone = 1 - 0.2778 = 0.7222

So,

Answer is:

0.7222

(d)

Draw 1: Red stone:

Red stone = 6

Green stone = 7

Blue stone = 5

Total stones = 18

So,

P(Draw 1: Red stone) = 6/18 = 0.3333

Draw 2: Blue stone:

Red stone = 5

Green stone = 7

Blue stone = 5

Total stones = 17

So,

P(Draw 2: Blue stone) = 5/17 = 0.2941

So,

the probability that you will pull out a blue stone this time = 0.3333 X 0.2941 = 0.0980

So,\Answer is:

0.0980