A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
a. 3/13
b. 4/13
c. 6/13
d. 9/13

Solution:

Consider S as the sample space

In a pack, there are 52 playing cards

n(S) = 52

Consider B as the event that the card drawn is a face card

In a pack, total face card = 12

n(B) = 12

So the probability of it being a face card is

P (B) = n(B)/ n(S)

= 12/52

= 3/13

Therefore, the probability of it being a face card is 3/13.

✦ Try This: A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a king is a. 1/13, b. 4/13, c. 6/13, d. 9/13

Consider S as the sample space

In a pack, there are 52 playing cards

n (S) = 52

Consider A as the event that the card drawn is king

n (A) = 4

So the probability of it being a king is

P (A) = n(A)/ n(S)

Substituting the values

= 4/52

= 1/13

Therefore, the probability of it being a face card is 1/13.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

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NCERT Exemplar Class 10 Maths Exercise 13.1 Sample Problem 5

A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is a. 3/13, b. 4/13, c. 6/13, d. 9/13

Summary:

A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is 3/13

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