Question

Two standard dice are rolled and their face values multiplied. What is the probability that the product is prime or ends in a 5?

Answer 1

Answer:

6/21

Step-by-step explanation:

1. First, check all the possible combinations for a pair of dice:

1-1

1-2 2-2

1-3 2-3 3-3

1-4 2-4 3-4 4-4

1-5 2-5 3-5 4-5 5-5

1-6 2-6 3-6 4-6 5-6 6-6

(Those are the numbers of the dice, separated by hyphons.)

2. Next, find out the products, since that is the info we need to go off of.

1

2 4

3 6 9

4 8 12 16

5 10 15 20 25

6 12 18 24 30 36

(those are all the products based on the same chart we saw above.)

3. Now, let's calculate the probability.

• Find the amount of prime numbers. (1, 2, 3, 5) Looks like there are four total.
• Find the amount of numbers that end in a five. (15, 25) There are two. I've skipped 5 because that is already on the list.
• Find the total amount of numbers. There are 21 in our case.

4. There are 6 numbers that will satisfy our needs. (prime or ending in 5)

There are 21 total.

6/21

If you need decimal form, there is a

0.2857 chance.

Hope this helped.

Answer 2

Answer:

$\frac{11}{36}$

Step-by-step explanation:

To find the probability that the product is prime or ends in  a 5, we need to look into the face value, the numbers that are prime when you multiply the face value are 6 and the numbers that end in a 5 are 5

Probability = required outcome / all possible outcome

In a probability, whenever you see the word 'or', you are to add

probability =  6/36  + 5/36    = 11/36