81.1k views
0 votes
Two 6-sided dice are rolled. Find the probability that exactly 1 die shows a 5.

Two 6-sided dice are rolled. Find the probability that exactly 1 die shows a 5.-example-1
User SourabhKus
by
3.1k points

1 Answer

2 votes

1) Let's begin by writing all the possible outcomes of those two dices between parentheses. The first number refers to the first dice, and the second one to the 2nd dice:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Note that there are 36 outcomes.

2) Now, let's focus on finding the number of favorable events:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

There are a total number of 10 favorable outcomes.

3) Therefore, we can write out the following probability:


undefined

User Sdellysse
by
3.3k points