Q24 of 46 Page 1

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn at random and are found to be both clubs. Find the probability of the lost card being of clubs.

OR


From a lot of 10 bulbs, which includes 3 defectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.

Let A: cards drawn are both club


E1:Lost card is club


E2 : Lost card is not a club



P(A/E1) = prob. Of drawing both club cards when lost card is club


P(A/E2) = prob. Of drawing both club cards when lost card is not club


By Bayes’ theorem,







OR


There are 3 defective bulbs and 7 non-defective bulbs.


Let X be the random variable which signifies the number of defective bulbs.


⇒ Then X can take values from 0,1,2 since bulbs are replaced


⇒


⇒


We have


⇒


⇒


⇒


∴ Required Probability distribution is



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