Question

An urn contains 9 red balls, 7 blue balls and 6 green balls. A ball is selected and its color is noted then it is placed back to the urn. A second ball is selected and its color is noted. Find the probability that the color of one of the balls is red and the color of the other ball is blue.

A. 0.2603
B. 0.2727
C. 0.4091
D. 0.3430

Answer 1

Ans: A) 0.2603

Note that here the selected ball is placed back into the urn so we have to deal with WITH REPLACEMENT problem.

Whlie working with replacement ,we have to use multinomial distribution.

The size of the sample space is

     .

Let X1 and X2 denote the number of red and  blue balls selected, respectively.

The Multinomial Theorem  is given as

Puting the values we have

P(X1 = X2   = 1 ) =

=   0.2603306

Hence option A) 0.2603.