Question

A card is drawn at random from an ordinary pack of 52 playing cards. What is the probability that it is a king; given that it is a face card? [a face card is either a jack, a queen or a king]. Select one:


a. 1/13


b. 1/3


c. 1/12


d. 1/4

Answer 1

Step-by-step explanation:

a) 1÷13

it's not sure

i think so

Answer 2

b. 1/3

The probability that it is a king; given that it is a face card si $\dfrac{1}{3}$

Explanation:

We know that , Total number of cards in a deck = 52

Number of face cards = 12  ( 4 King + 8 others)

The probability that a card is face card P(Face card)= $\dfrac{\text{Total face cards}}{\text{Total cards}}$

$=\dfrac{12}{52}=\dfrac{3}{13}$

Number of cards are king = 4

The probability that a card is face card are King :

P( Face card and king )= $\dfrac{4}{52}=\dfrac{1}{13}$

Using conditional probability formula ,

P(a king | face card) = $\dfrac{\text{P( Face card and king )}}{\text{ P(Face card)}}$

$=\dfrac{\dfrac{1}{13}}{\dfrac{3}{13}}=\dfrac{1}{3}$

Hence, the probability that it is a king; given that it is a face card = $\dfrac{1}{3}$

#Learn more :

What is mean by conditional probability

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