Question

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 1

Answer: 1/5

Step-by-step explanation:

P(both are Orange)

P(at least one is orange)

By using conditional probability:

-The P(both are Orange) is (2C2)/4C2)=1/6

-at least one orange is 1 - 1/6=5/6

P(both are Orange / at least one is orange)=(1/6) / (5/6)

=6/30

=1/5

Answer 2

Answer:

0.2

Step-by-step explanation:

An urn contains 2 orange balls and 2 blue balls.

let O represent orange balls

Let B represent blue balls

Probability of at least one orange ball

P(O1) = 2/4 = 1/2

P(B1) = 2/4 = 1/2

After 1 blue ball has been drawn, we have 2 orange balls among the 3 remaining balls

P(O2|B1) = 2/3

After 1 orange ball has been drawn, we have 1 orange ball and 2 blue balls among the remaining 3 balls

P(O2|O1) = 1/3

P(B2|O1) = 2/3

Using general multiplication, we have

P(B1 n O2) = P(B1) * P(O2|B1)

= 1/2 * 2/3 = 1/3

P(O1 n O2) = P(O1) * P(O2|O1)

= 1/2 * 1/3 = 1/6

P(O1 n B2) = P(O1) * P(B2|O1)

= 1/2 * 2/3 = 1/3

P(at least one orange) = P(B1 n O2) + P(O1 n O2) + P(O1 n B2)

= 1/3 + 1/6 + 1/3

= 5/6

Using conditional probability

P(both orange | at least one orange) = P(both orange and at least one orange) / P(at least one orange)

= P(O1 n O2) / P(at least one orange)

= 1/6 / 5/6

= 1/5

= 0.2