Question

in a well-shuffled, standard 52 card deck, what is the probability of a card being a jack, given that it is a face card? answer choices are in a percentage format, rounded to the nearest whole number.

Answer 1

Answer:

33%

Step-by-step explanation:

let's say the card being a jack is A and the card being a face card is B

probability of A given B (conditional probability) = (probability of A and B)/(probability of B)

probability of the card being a jack AND a face card: 4/52 = 1/13, as all jacks are face cards

probability of there being a face card: 12/52 = 3/13, as there are 12 face cards in a deck

probability of a card being a jack given that it is a face card:

(probability of A and B)/(probability of B)= (1/13) / (3/13) = 1/3 ≈ 33%