Question

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?

Answer 1

= 0.7143

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