Urn A consists 3 blue and 4 green balls while another urn B consists 5 blue and 6 green balls. One ball is drawn at random from one of the urns and it is found to be blue. Determine the probability that it was drawn from urn B?

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  1. \(\frac{{68}}{{35}}\)
  2. \(\frac{{35}}{{68}}\)
  3. \(\frac{{34}}{{77}}\)
  4. \(\frac{{77}}{{34}}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{{35}}{{68}}\)
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Given:

Urn A consists 3 blue and 4 green balls 

Urn B consists 5 blue and 6 green balls

One ball drawn at random from one of the urns was blue

Concept:

Baye's Theorem :

Solution:

Let B be the event that the ball drawn is blue and E1 be the event that the ball is drawn from urn 1 and Ebe the event that the ball is drawn from urn 2.

∴ P(B) = P(B ∩ E1) + P(B ∩ E2)

⇒ P(B) = \(\frac{1}{2}\times\frac{3}{7} + \frac{1}{2}\times\frac{5}{11} \)

= 34/77

∴ P(E2/B) = \(\frac{P(E_1 \cap B)}{P(B)} = \frac{P(E_2) P(B/E_2))}{P(B)}\)

\(\frac{\frac{1}{2}\times \frac{5}{11}}{\frac{34}{77}}\)

= 35/68

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