Probability ncert solutions Chapter 15 Exercise 15.1 Question 14
14. A card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red color (ii) a face card (iii) a red face card
(iv) the jack of hearts (v) a spade (vi) the queen of diamonds
Solution (i)
Let E be the event of drawing a king of red color
Number of outcomes favorable to event E=2 {There are two red kings in a deck of 52 cards}
Total number of possible outcomes=52 {There are total of 52 cards}
P(E)=(Number of outcomes favorable to event E)/(Total number of possible outcomes)=2/52=1/26
(ii)
Let F be the event of drawing a face card.
Number of outcomes favorable to event F=12 {There are 12 face cards in a deck of 52 cards}
Total number of possible outcomes=52 {There are total of 52 cards}
P(F)=(Number of outcomes favorable to event F)/(Total number of possible outcomes)=12/52=3/13
(iii)
Let A be the event of drawing a red face card.
Number of outcomes favorable to event F=6 {There are 6 red face cards in a deck of 52 cards}
Total number of possible outcomes=52 {There are total of 52 cards}
P(A)=(Number of outcomes favorable to event A)/(Total number of possible outcomes)=6/52=3/26
(iv)
Let B be the event of drawing jack of hearts.
Number of outcomes favorable to event B=1 {There is 1 jack of hearts in a deck of 52 cards}
Total number of possible outcomes=52 {There are total of 52 cards}
P(B)=(Number of outcomes favorable to event B)/(Total number of possible outcomes)=1/52
(v)
Let C be the event of drawing a spade.
Number of outcomes favorable to event C=13
{There are 13 spade cards in a deck of 52 cards}
Total number of possible outcomes=52 {There are total of 52 cards}
P(C)=(Number of outcomes favorable to event C)/(Total number of possible outcomes)=13/52=1/4
(vi)
Let D be the event of drawing a queen of diamonds.
Number of outcomes favorable to event D=1 {There is 1 queen of diamonds in a deck of 52 cards}
Total number of possible outcomes=52 {There are total of 52 cards}
P(D)=(Number of outcomes favorable to event D)/(Total number of possible outcomes)=1/52
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