Question

A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. Two people are drawing from one jar one after the other. Determine the probability of the following events occurring.

A) the first person draws and keeps a yellow marble and then the second person draws a green marble

B) the first person draws and keeps a blue marble and then the second person draws a red marble

C) the first person draws and keeps the green marble and then the second person draws anything other than the red marble

D) the first person draws and keeps a red marble and then the second person draws a red marble

E) the first person draws and keeps a blue marble and then the second person draws a blue marble

Answer 1

RED (R) = 1

GREEN (G) = 3

BLUE(B)=2

YELLOW (Y)=4

TOTAL = 1+3+2+4 = 10

A) P( the first person draws and keeps a yellow marble and then the second person draws a green marble)

= P( Y) * P(G)

= (4/10)*(3/9)

=0.1333

B) P( the first person draws and keeps a blue marble and then the second person draws a red marble)

= P(B) * P( R)

=(2/10)*(1/9)

=0.0222

C) P( the first person draws and keeps the green marble and then the second person draws anything other than the red marble)

= P( G) * P(R')

=P(G) * (1-P(R))

= (3/10) * ( 1- (1/9))

=(3/10) * (8/9)

=0.2667

D) P( the first person draws and keeps a red marble and then the second person draws a red marble)

= P(R) * P(R)

= (1/10) * 0 ; as there is only 1 red marbel that is already kept by the first person

=0

E)P( the first person draws and keeps a blue marble and then the second person draws a blue marble)

= P(B) * P(B)

=(2/10) * (1/9)

=0.0222