Conditional Probability & Bayes Theorem: JEE Questions & Solutions

A bag contains 10 balls out of which k are red and (10-k) are black, where 0 k 10. If three balls are drawn at random without replacement…

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that…

If A and B are two events such that P(A B) = 0.1, and P(A B) and P(B A) are the roots of the equation 12x^2 - 7x + 1 = 0, then the value of…

Bag B1 contains 6 white and 4 blue balls, Bag B2 contains 4 white and 6 blue balls, and Bag B3 contains 5 white and 5 blue balls. One of…

Given three identical bags each containing 10 balls, whose colours are as follows: Bag I 3 Red 2 Blue 5 Green Bag II 4 Red 3 Blue 3 Green…

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of…

A bag contains 19 unbiased coins and one coin with heads on both sides. One coin is drawn at random and tossed, and heads turns up. If the…

If A and B are two events such that P(A) = 0.7, P(B) = 0.4 and P ( A B) = 0.5, where B denotes the complement of B, then P ( B ( A B)) is…

Bag A contains 3 white and 7 red balls, and bag B contains 3 white and 2 red balls. One bag is selected at random, and a ball is drawn. The…

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2…

Three urns A, B, and C contain 7 red, 5 black; 5 red, 7 black; and 6 red, 6 black balls, respectively. One of the urns is selected at…

The urns A, B, and C contain 4 red, 6 black; 5 red, 5 black, and red; 4 black balls respectively. One of the urns is selected at random,…

25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non-smoker. If a person is diagnosed…

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at…

In a bolt factory, machines A, B, and C manufacture respectively 20, 30, and 50 of the total bolts. Of their output, 3, 4, and 2 are…