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Bag 1 contains 4 white and 6 black balls while another Bag 2 contains 4 white and 3 black balls. One ball is drawn at random from one of the bags and it is found to be black. Find the probability that it was drawn from Bag 1.

Correct Answer: 7/12
Let E1 = event of choosing the bag 1, E2 = event of choosing the bag 2. Let A be event of drawing a black ball. P(E1) = P(E2) = 1/2. Also, P(A|E1) = P(drawing a black ball from Bag 1) = 6/10 = 3/5. P(A|E2) = P(drawing a black ball from Bag 2) = 3/7. By using Bayes’ theorem, the probability of drawing a black ball from bag 1 out of two bags is-: P(E1|A) = P(E1)P(A|E1)/( P(E1)P(A│E1)+P(E2)P(A|E2)) = (1/2 × 3/5) / ((1/2 × 3/7)) + (1/2 × 3/5)) = 7/12.

Bag 1 contains 3 red and 5 black balls while another Bag 2 contains 4 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it is drawn from bag 2.

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

একটি থলেতে 4 টি সাদা এবং 2 টি কালো বল আছে। অপর একটি থলেতে 3 টি সাদা ও 5 টি কালো বল আছে। যদি প্রত্যেক থলে হতে একটি করে বল উত্তোলন করা হয়, তবে বলদ্বয় সাদা হওয়ার সম্ভাবনা কত? (A bag contains 4 white and 2 black balls. Another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, what is the probability that both balls are white?)

A bag contains 6 red balls 11 yellow balls and 5 pink balls. If two balls are drawn at random from the bag. One after another what is the probability that the first ball is red and second ball is yellow?

A bag contains 4 red balls, 6 blue balls and 8 pink balls. One ball is drawn at random and replaced with 3 pink balls. A probability that the first ball drawn was either red or blue in colour and the second drawn was pink in colour ?

Statements followed by some conclusions are given below. Statements:
1. A bag has 2 white, 3 black, 4 red and 6 green balls.
2. 2 balls are selected at random from the bag. Conclusions:
1. The probability that a black ball is selected is 1/5.
2. The probability that a red ball is selected is 6/15. Find which of the conclusions logically follows from the given statements.

A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag.
Find the probability that one ball is red and one is green.

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A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?