Question

An urn contains 5 blue marbles and 4 yellow marbles. One marble is​ removed, its color​ noted, and not replaced. A second marble is removed and its color is noted.

(a) What is the probability that both marbles are blue? yellow​?
​(b) What is the probability that exactly one marble is blue​?

Answer 1

(a)The probability that both marbles are blue=5/18

The probability that both marbles are yellow=1/6

(b)The probability that exactly one marble is blue​=5/9

Explanation:

Blue marbles=5

Yellow marbles=4

Total marbles=5+4=9

(a)

Probability of drawing first blue marble=5/9

Probability of drawing second blue marble without replacement=4/8

The probability that both marbles are blue

`=(5)/(9)* (4)/(8)=(5)/(18)`

Probability of drawing first yellow marble=4/9

Probability of drawing second yellow marble without replacement=3/8

The probability that both marbles are yellow

`=(4)/(9)* (3)/(8)=(1)/(6)`

(b)

The probability that exactly one marble is blue​

=Probability of first blue marble (Probability of second yellow marble)+Probability of first yellow marble (Probability of second blue marble)

The probability that exactly one marble is blue​

=
`(5)/(9)* (4)/(8)+(4)/(9)* (5)/(8)`

=
`(5)/(18)+(5)/(18)`

=
`(10)/(18)=(5)/(9)`