Question

15. If you are randomly sampling one at a time with replacement for a bag that contains eight blue marbles, seven red marbles, and five green marbles, what is the probability of obtaining

a. A blue marble in one draw from the bag?

b. Three blue marbles in three draws from the bag?

c. A red, a green, and a blue marble in that order in three draws from the bag?

d. At least two red marbles in three draws from the bag?

16. Answer the same questions as in problem 15, except sampling is one at a time without replacement.

Answer 1

15)

as the experiment is with replacement probability of blue marble =8/20=0.4 ; of red marble =7/20=0.35

and of green marble=5/20=0.25

a) P( A blue marble in one draw from the bag) =8/20=0.4

b)P(Three blue marbles in three draws from the bag)=(0.4)³ =0.064

c)

P(A red, a green, and a blue marble in that order in three draws from the bag)=0.4*0.35*0.25=0.035

d)

PAt least two red marbles in three draws from the bag)=P(2 red)+P(3 red)

= =0.2818

16)

a)

P( A blue marble in one draw from the bag)=8/20=0.4 (as 8 blue marble out of total 20 marbles)

b)

P(Three blue marbles in three draws from the bag)=(8/20)*(7/19)*(6/18)=0.0491

c)A red, a green, and a blue marble in that order in three draws from the bag=(7/20)*(5/19)*(8/18)

=0.0409

d)

At least two red marbles in three draws from the bag=P(2 red draws)+P(3 red draws)

=

=0.2702