Urn A consists of 3 blue and 4 green balls while another urn B consists of 5 blue and 6 green balls. One ball is drawn at random from one of the urns - Mathematics MCQ Mathematics Mock Test - 9 2026 | ExamTest.live

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Urn A consists of 3 blue and 4 green balls while another urn B consists of 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?

Solution & Step-by-step Explanation

Let E_{1} be the event of selecting Urn A, E_{2} be the event of selecting Urn B, and B be the event of drawing a blue ball. P (E_{1}) = P (E_{2}) = 1/2 . P (B ∣ E_{1}) = 3/7 and P (B ∣ E_{2}) = 5/11 .We need to find P (E_{2} ∣ B) using Bayes' Theorem: P (E_{2} ∣ B) = \frac{P ( E _{2} ) P ( B ∣ E _{2} )}{P ( E _{1} ) P ( B ∣ E _{1} ) + P ( E _{2} ) P ( B ∣ E _{2} )} P (E_{2} ∣ B) = \frac{\frac{1}{2} \cdot \frac{5}{11}}{\frac{1}{2} \cdot \frac{3}{7} + \frac{1}{2} \cdot \frac{5}{11}} = \frac{\frac{5}{11}}{\frac{3}{7} + \frac{5}{11}} P (E_{2} ∣ B) = \frac{\frac{5}{11}}{\frac{33 + 35}{77}} = \frac{5}{11} \cdot \frac{77}{68} = \frac{5 \times 7}{68} = \frac{35}{68}

Try it yourself before checking the explanation above.

Urn A consists of 3 blue and 4 green balls while another urn B consists of 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?

68/35

35/68

34/77

77/34

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