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

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.

Answer 2

Answer:
`(2)/(3)`

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)=
`\frac{\text{Number of face cards }}{\text{Total cards}}`

`\\\\=(12)/(52)=(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 )=
`\frac{\text{Number of face cards are not King}}{\text{Total cards}}`

`\\\\=(8)/(52)=(2)/(13)`

Using conditional probability formula ,

`\text{P(Not king}|\text{ Face card})=\frac{\text{P( Face card and not king )}}{\text{ P(Face card)}}`

`=((2)/(13))/((3)/(13))=(2)/(3)`

Hence, the probability that it is not a king given that it is a face card
`=(2)/(3)`