**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