Question

A bag contains 6 blue balls, 2 red balls and 1 black ball. If two are selected at random, find the probability of obtaining the black ball.

Answer 1

Total number of balls = 6+2+1

=9

According to question , It is given that 2 balls are selected randomly out of 9 balls .

Then number of ways of of selecting 2 ball is given by

=C(9,2)

=9!/(2!×7!)

=9×8/2

=36

Next we need to find the number of ways in which we can select 1 black ball and other ball can be either blue or red

=C(1,1){ c(6,1)+c(2,1)}

=1×(⁶c₁+²c₁)

Here we can choose 1 black ball in only way, i.e. one way . and another ball can be choose from either 6 balls or 2 balls

On solving ,we get

= 6+2

=8

Now probability =number of favourable outcomes / number of total outcomes

Probability =8/36

=4/9

=0.4444

conclusion - probability =0.4444

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