Pick a card from 52, P(red) Step by Step

Step by step

The question

Question: A card is picked from a deck of 52 cards.

What is the probability it is a red card?

The probability is a fraction: the outcomes we want, over all the outcomes.

P(red) = we wantall

P stands for probability.

P = probability

1 Count all outcomes

A deck has 52 cards.

all = 52

It has 4 suits: hearts, diamonds, clubs and spades.

Each suit has 13 cards.

4 times 13 is 52.

4 suits: hearts, diamonds, clubs, spades

13 in each: A, 2 to 10, J, Q, K

4 × 13 = 52

2 Count the ones we want

Red cards: 26.

red: 2 suits of 13

That is 26 outcomes we want.

we want = 26

3 Write the fraction

26 we want, out of 52.

So the probability is 26/52.

P(red) = 2652

4 Simplify

Both 26 and 52 can be divided by 26.

That makes it simpler.

P(red) = 26 ÷ 2652 ÷ 26

So it is 1/2.

P(red) = 12

5 As a percent

Percent means out of 100.

We make the bottom 100: times 50, top and bottom.

50 out of 100 is 50%.

P(red) = 50100 = 50%

1 × 50 = 50

2 × 50 = 100

6 Check

Let's check with the others.

52 minus 26 is 26.

26/52 plus 26/52 is 52/52: that is 1, all of them.

So the answer is right!

P(red) + P(not red) = 2652 + 2652 = 5252 = 1

Let's look back.

First: count all outcomes.

Then: count the ones we want.

Then: write the fraction.

Then: simplify.

Then: as a percent.

Last: check.

Answer