Question

A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting

· an odd prime number under 10 given the card is a club. (1 is not prime.)
· a Jack, given that the card is not a heart.
· a King given the card is not a face card.


Show step by step work. Give all solutions exactly in reduced fraction form.

Answer 1

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There are three odd prime numbers under 10, they are : 3,5,7
Given the card is a club - there are a total of 13 cards -
so the probability to select a card with prime number
under 10 given it is a club is 3/13

*
Given the card is not a heart means we are dealing with 52 - 13 = 39 cards,
and three of them are jacks -
so the probability to select one of the 3 jacks
from the 39 non-heart cards is 3/39

*
A King is a face card, so the probability of selecting a king - given
the card is not a face card is 0.