PROBLEM 7E

An urn contains four colored balls: two orange and two blue. Two balls are selected at random without replacement, and you are told that at least one of them is orange. What is the probability that the other ball is also orange?

Answer:

Step 1 of 3:

Given that, an urn contains four colored balls: Two orange and two blue. Two balls are selected at random without replacement and then at least one of them is orange.

Here the aim is to find the probability that the other ball is also orange.

Step 2 of 3:

Let A = {at least one ball is orange}

Let B = { both balls are orange}

Total ways of selecting 2 balls =

= 6

Then, P( at least one of them is orange) = P(A)

P(A) = 1- P(none is orange)

= 1-

=

Therefore,

P( both ball orange/at least one of them is orange) = P(B/A)

Thus,

P(B/A) =

=

=