# Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

When two dice are thrown simultaneously, the probability of getting two numbers whose product is even is 3/4. Probability refers to the possibility of an event happening. There are various variables that can impact this possibility. The range in which an event can occur or not is between 0 and 1 where 0 means an event is not likely to occur whereas 1 means an event is likely to occur.

## Probability of Getting Numbers Whose Product is Even

In the case of an event, the probability of something happening depends on two factors. These factors are the total number of outcomes and the number of favorable outcomes. The formula to calculate the probability of an event denoted by P (E) is –

P(E) = Total number of outcomes/Number of favorable outcomes

Probability is a chance of something within the range of 0 and 1. While 0 means that it is unlikely an event will happen. 1 is the likelihood that an event can happen.

### Solution

When two dice are rolled, the probability of getting two numbers whose product is event depends on the total number of outcomes and the total number of favorable outcomes. Here, we have two dice which means our total number of outcomes will be –

Total number of outcomes = 6×6 = 36

Now, we need to find the number of favorable outcomes, which are getting two numbers whose products are even.

So, our favorable outcomes are – (1,2), (1,4), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (3,4), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,2), (5,4), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5) and (6,6)

Number of favorable outcomes = 27

Now, keeping the formula discussed above in mind,

36/27 = 3/4

Thus, the probability of getting two numbers with an even sum when two dice are rolled is 3/4.

Summary:

## Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

The probability of such an event happening is 3/4. To calculate the probability of an event happening, it is important to consider the total number of outcomes and the number of favorable outcomes. This way, the actual probability of an event can be calculated.

Related Questions:

POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com