Two identical urns contain balls. Urn1 has 3 red balls, 3 green balls, and 3 blue balls. Urn2 has 4 red balls and 6 blue balls. An urn is chosen at random and a ball is drawn at random from this urn. If the ball turns out to be blue, what is the probability that this is Urn1?

= 0.7143

Step-by-step explanation:

P (Urn 1) = 1 / 2, P (urn 2) = 1/2

P (Blue ball from urn 1) = 3 / 9 = 1/3

P (Blue ball from urn 2) = 6 / 10 = 3/5

P (Urn 1 | Blue ball) = P (Urn 1 and Blue ball) / P (Blue ball)

By baye's theorem

= P (Urn 1 and Blue ball) / [ P (Urn 1 and Blue ball) + P (Urn 2 and Blue ball) ]

= 1/2 * 3/9 / [ 1/2 * 3/9 + 1/2 * 6/10 ]

solving we get

= 0.7143