Answer to Question #324197 in Statistics and Probability for Rival

Question

Suppose a box contains 20 red marbles, 12 blue

marbles, 8 green marbles, and 10 yellow marbles. If

you randomly select one marble from the box.

(a) what is the probability that you will have a red

marble?

(b) what is the probability that you will have a green

marble?

(c) what is the probability that you will have a red or

green marble?

(d) what is the probability that you will have a red and

yellow marble?

(e) what is the probability that you will have a red

marble with replacement?

(f) what is the probability that you will have a blue

marble without replacement?

(g) what is the probability that you will have a yellow

marble with replacement?

(h) what is the probability that you will have a green

marble with replacement?

Answer 1

There are 20+12+8+10=50 marbles altogether.

a. P(red)=20/50=0.4

b. P(green)=8/50=0.16

c. P(red or green)=P(red)+P(green)=0.4+0.16=0.56

d. If we take 2 marbles P(yellow)=10/50=0.2

P(yellow and red)=P(yellow)P(red)=0.2$\times$ 0.4=0.08

If we take 1 marble, given in the question, P(yellow and red)=0

e. If we take 1 marble, given in the question, then P(red with replacement)= P(red without replacement)=0.4

f. P( blue with replacement)=P(blue without replacement)=12/50=0.24

g.P(yellow with replacement)= P(yellow without replacement)=10/50=0.2

h. P(green with replacement)=P(without replacement)=8/50=0.16