Question

Lenny rolls two number cubes. What is the probability that the sum of the numbers Lenny rolls is either 4 or 7?

Answer 1

Probability of an event =

(number of ways the event can happen) / (total number of possible outcomes) .

Well, the total number of possible outcomes is easy. It's

(6 possibilities for the first cube) x (6 possibilities for the 2nd cube)

= 36 total possible ways for two cubes to roll.

Now, how many of those possibilities show either 4 or 7 ?

Well, here's how a 4 can come up:

1 . . . 3

2 . . . 2

3 . . . 1

and here's how a 7 can come up:

1 . . . 6

2 . . . 5

3 . . . 4

4 . . . 3

5 . . . 2

6 . . . 1 .

So there are 9 ways all together for Lenny to be successful.

The probability is (9/36) .

That's 1/4 , or 25% .

Answer 2

$|\Omega|=6^2=36\\ |A|=\underbrace{3}_{\text{the sum is 4}}+\underbrace{6}_{\text{the sum is 7}}=9\\\\ P(A)=\dfrac{9}{36}=\dfrac{1}{4}=25\%$