SOLUTION: As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts

Question 1024511: As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King).
If you select a card at random, what is the probability of getting:
1) A(n) 2 of Hearts?
2) Spades or Hearts?
3) A number smaller than 4 (counting the ace as a 1)?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King).
If you select a card at random, what is the probability of getting:
1) A(n) 2 of Hearts?
2) Spades or Hearts?
3) A number smaller than 4 (counting the ace as a 1)?

Solution:
In probability, it is often assumed (but not stated) that all outcomes are equally probable. This is the case with drawing cards from a deck, or throwing a (fair) die, or tossing a (fair) coin.
The first step in answering questions of equi-probability is to examine the question to see if it is indeed a case of equi-probability. If it is not stated, the situation becomes an assumption and must be restated in the answer.

Assuming the probability of drawing any card out of the given deck is equally probable, then
(1) the probability of drawing a given card is P(2❤)1/52.
(2) There are 13 spades, and 13 hearts. The probability of getting either spades or hearts is the sum of the two. This addition rule applies when outcomes are mutually exclusive (ME), i.e. they do not overlap.
So P(♠∪♥)=(13+13)/52=1/2
(3) A number smaller than four
We count 3 cards smaller than 4, namely 3,2,1(Ace).
Since there are four suits, so there are 3*4=12 such cards.
Therefore the corresponding probability is
P(<4)=12/52=3/13

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