Pick a card from 52, P(king or queen) 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 king or a queen?

1 Find each one

Call king A.

There are 4.

A = king → 4 cards

P stands for probability.

There are 52 outcomes in all.

P = probability, all = 52

Call queen B.

There are 4.

B = queen → 4 cards

Is anything in both?

No.

Nothing is A and B at the same time.

A and B = nothing

2 Draw a Venn diagram

3 Add them

A or B: we add them.

Nothing is counted twice.

P(A or B) = P(A) + P(B)

When two things can't happen together, we call them mutually exclusive.

mutually exclusive:

they can't happen together

In numbers: 4/52, plus 4/52.

P(A or B) = 452 + 452

Careful!

Nothing is in both, so there is nothing to take away.

Careful: nothing in both: nothing to take away

Same bottoms: we add and take away the tops.

P(A or B) = 4 + 452

4 plus 4 is 8.

So it is 8/52.

P(A or B) = 852

4 Simplify

Both 8 and 52 can be divided by 4.

That makes it simpler.

P(A or B) = 8 ÷ 452 ÷ 4

So it is 2/13.

P(A or B) = 213

5 Check

Let's check: we count what is inside the circles.

4 plus 4 is 8.

8 out of 52.

The same.

So the answer is right!

in the circles: 4 + 4 = 8 → 852

Let's look back.

First: find each one.

Then: draw a Venn diagram.

Then: add them.

Then: simplify.

Last: check.

Answer