Question

Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles.

Find the following probabilities of Dustin drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.

a) A Blue, then a red =

b) A red, then a white =

c) A Blue, then a Blue, then a Blue =

Answer 1

A.

`(6)/(55)`

B.

`(6)/(55)`

C.

`(4)/(165)`

Explanation:

Dustin has a bag of marbles with 4 blue marbles, 4 white marbles, and 3 red marbles. There are 11 marbles in total.

A. The probability that the first marble drawn is blue marble is

`(4)/(11),`

the probability that the second marble drawn is red marble is

`(3)/(10)`

The probability that the first marble drawn is blue and the second is red is

`(4)/(11)\cdot (3)/(10)=(12)/(110)=(6)/(55)`

B. The probability that the first marble drawn is red marble is

`(3)/(11),`

the probability that the second marble drawn is white marble is

`(4)/(10)`

The probability that the first marble drawn is red and the second is white is

`(3)/(11)\cdot (4)/(10)=(12)/(110)=(6)/(55)`

C. The probability that the first marble drawn is blue marble is

`(4)/(11),`

the probability that the second marble drawn is blue marble is

`(3)/(10),`

the probability that the third marble drawn is blue marble is

`(2)/(9),`

The probability that the first, second and third marbles drawn are blue is

`(4)/(11)\cdot (3)/(10)\cdot (2)/(9)=(24)/(990)=(4)/(165)`