Probability

From a pack of 52 cards, a blackjack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is
(i) a black card
(ii) a king
(iii) a red queen.

Solution: Total number of cards = 52-4 = 48 [∡4 cards fell down] So number of possible outcomes = 48 (i) Let E be the event of getting black card. There will be 23 black cards since a black jack and...

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A box contains 15 cards numbered 1, 2, 3,…..15 which are mixed thoroughly. A card is drawn from the box at random. Find the probability that the number on the card is :
(v) divisible by 3 or 2
(vi) a perfect square number.

(v) Let E be the event of getting the number on the card is divisible by 3 or 2 Outcomes favourable to E are {2,3,4,6,8,9,10,12,14,15} Number of favourable outcomes = 10 P(E) = 10/15 = 2/3 Hence the...

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A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (shown in the adjoining figure) and these are equally likely outcomes. What is the probability that it will point at
(iii) a number greater than 2?
(iv) a number less than 9?

(iii) Let E be the event of arrow pointing a number greater than 2. Outcomes favourable to E are {3,4,5,6,7,8} Number of favourable outcomes = 6 P(E) = 6/8 = 3/4 Hence the probability of arrow...

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12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Solution: Number of defective pens = 12 Number of good pens = 132. Total number of pens = 132+12 = 144 Probability of getting a good pen, P(E) P(E) = 132/144 = 11/12 Hence the required probability...

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