four red cards are numbered 1,2,3, and 4. Three black cards are numbered 5,6, and 7.

Question

The cards are placed in a box and one card is selected at random.  What is the probability that a red card was selected given that the number on the card was an even number

Answer 1

Jaz,

 

Let's follow the problem from the beginning:

 

- There are four red cards:  R1, R2, R3, and R4

- There are three black cards:  B5, B6, and B7

 

We draw a card.  We're told that it's even.

 

1. Which of the cards might we have drawn?  I think there are three of them...

2. Of those even cards, how many of them are red?

 

The probability you're looking for is the number of possible red even cards, but you already know it's even.  So, there aren't 7 total cards to deal with anymore.  There are three.  Of those three even cards, if you can count how many are red, then the red ones, out of three even ones, would be your answer.  So, it's a fraction, something divided by 3...

 

Hope this helps.

 

Answer 2

Probability = successes / total

 

Two cards are both red and have even numbers.

 

2 / 7