Question

Lewis rolls a number cube and then chooses a card from a set of cards numbered 1 through 5. What is the probability that he will roll an even number and choose an even numbered card?

Answer 1

`(1)/(5)=0.2`

Explanation:

The general formula for a probability is:

`P=(FavorableEvent)/(TotalEvents)`

The favorable events for the cube to fall in a even number are:

2, 4, and 6 ⇒ 3 favorable events

and in the cube the total events are:

1, 2, 3, 4, 5, 6 ⇒ 6 total events

So the probability of rolling an even number in the cube is:

`P=(3)/(6)\\\\\\ P=(1)/(2)`

Now we do something similar to find the probability to choose a card with an even number.

The favorable events for an even numbered card are:

2, 4 ⇒ 2 favorable events

and the total number of events in the cards is:

1, 2, 3, 4, 5 ⇒ 5 total events

Thus, the probability to choose an even numbered card (according to the probability formula) is:

`P=(2)/(5)`

And finally, since we want both things to happen we must multiply both obtained probabilities:

• the probability that he will roll an even number and choose an even numbered card:

`P=(1)/(2)*(2)/(5) \\ \\P=(2)/(10) \\\\P=(1)/(5) =0.2`

The probability is 1/5 which is equal to 0.2 or 20%