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: (Round to 4 decimal places where possible)a) A 2 of Hearts? b) A Spade or Heart? c) A number smaller than 3 (counting the ace as a 1)?

Question
Asked Nov 15, 2019
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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: (Round to 4 decimal places where possible)

a) A 2 of Hearts? 

b) A Spade or Heart? 

c) A number smaller than 3 (counting the ace as a 1)? 

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Expert Answer

Step 1

In a pack of card, 26 red and 26 black.

In 26 red cards, 13 heart cards and 13 diamond cards.

In 26 black cards, 13 club cards and 13 spade cards. 

Therefore, the total number of cards in a pack is 52.

The formula for finding probability is shown bellows:

Number of favorable outcomes
Probability =
Total number of outcomes
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Number of favorable outcomes Probability = Total number of outcomes

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Step 2

a)

The number of heart is 13. In that, only one card has number 2. The total number of cards in a pack is 52.

Therefore, the probability of g...

13
P(Spade or Heart
13
52 52
: Hearts and spades are mutually exclusive
26
52
1
2
-0.5000
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13 P(Spade or Heart 13 52 52 : Hearts and spades are mutually exclusive 26 52 1 2 -0.5000

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