Question

In a standard deck of cards, the jack, queen, and king are "face cards." you draw a card from a standard deck. your friend peeks and lets you know that your card is a face card. what is the probability that it is not a king given that it is a face card? leave your answer as a fraction

Answer 1

Answer: $\dfrac{2}{3}$

Step-by-step explanation:

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)= $\dfrac{\text{Number of face cards }}{\text{Total cards}}$

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

Number of cards are not king = 8

The probability that a card is face card are not King :

P( Face card and not king )= $\dfrac{\text{Number of face cards are not King}}{\text{Total cards}}$

$\\\\=\dfrac{8}{52}=\dfrac{2}{13}$

Using conditional probability formula ,

$\text{P(Not king}|\text{ Face card})=\dfrac{\text{P( Face card and not king )}}{\text{ P(Face card)}}$

$=\dfrac{\dfrac{2}{13}}{\dfrac{3}{13}}=\dfrac{2}{3}$

Hence, the probability that it is not a king given that it is a face card $=\dfrac{2}{3}$

Answer 2

If the Ace is a face card, then the answer will be 16/52 or 4/13 simplified.
If the Ace is NOT a face card, then the answer will be 12/52 or 3/13 simplified.