Question

Two fair dice are rolled. Find the odds for and the odds against getting a 3 and an even number.

Answer 1

The probability of getting a 3 and an even number = $\frac{1}{12}$

Step-by-step explanation:

Given,

Two fair dice are rolled.

To find the probability of getting a 3 and an even number.

Formula

The probability of an event = the possible outcomes ÷ total number of outcomes.

Now,

The total outcomes are =

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

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

(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) = 36

Required outcomes = (3, an even number) = (3,2),(3,4),(3,6) = 3

Hence,

The probability of getting a 3 and an even number = $\frac{3}{36} = \frac{1}{12}$