SOLUTION: Find the probability of neither a 5 or spade from a deck of cards

Question 1012847: Find the probability of neither a 5 or spade from a deck of cards
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
Find the probability of neither a 5 or spade from a deck of cards

Solution:

A standard deck of cards has 52 cards.

We will first find the number of cards that are either a 5 or a spade:
There are 4 5's (one for each suit) and 13 spades.
However, the 5 of spades has been counted two times, so the number of cards that are either 5 or a spade equals 4+13-1=16.

There are then 52-16=36 cards that are neither 5 nor spades.

The probability of drawing neither a 5 nor a spade from a standard deck is therefore
P(~5∧~spade)=36/52=9/13
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