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
