Two dice are thrown simultaneously. What is the probability of getting

Question

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

A)

B)

C)

D)

E)

chetan2u · Answer

Easier way is to find ways of ODD product.. 
each dice can show 1,3 or 5..
so ways of getting ODD product=  3*3=9 
Total ways to choose two numbers=  6*6=36

ways of picking numbers such that product is even = 36-9=27

probability of picking even product =  \frac{27}{36}=\frac{3}{4} 
B

OR second way..

ways of getting even product..

1)first dice even number - 2,4 or 6- 3 ways
for these three even numbers, second dice can be any of 6 numbers - 6 ways
total ways = 3*6=18

2) first dice odd number = 1,3, or 5 -- 3 ways
for these three odd numbers, second dice has to throw even numbers so 2,4,6 - 3 ways
total 3*3 = 9 ways

total ways = 18+9=27
total ways of picking any two numbers = 6*6=36

prob = 27/36=3/4
B

viv007 · Answer

Probability of both dice to be odd is = 3/6 * 3/6
 = 1/4
So probability of even = 1- probability of odd 
 = 1-1/4
 = 3/4

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CrackverbalGMAT · Answer

Hi,

While dealing with complex events in probability, the best way is to use the below equation to set up the question.

Probability (Complex event) = Probability (Individual Events) * arrangement

The complex event should always be represented by a set of alphabets, for example, if we need to find the probability of getting two heads and a tail when we toss a coin 3 times, then the probability can be represented as P(HHT).

P(HHT) = 1/2 * 1/2 * 1/2 * 3!/2! (3!/2! -----> arrangement of the word HHT)
P(HHT) = 3/8

Similarly here we need the probability of the product being even. There will be two cases here:

1. One number is even and one number odd, let us represent this as P(EO)

OR

2. Both numbers are even, let us represent this as P(EE)

P(EO) = 3/6 * 3/6 * 2! ----> 1/2

OR

P(EE) = 3/6 * 3/6 * 2!/2! -----> 1/4

1/2 + 1/4 = 3/4

Hope this helps!

BrushMyQuant · Answer

Given that Two dice are thrown simultaneously and we need to find What is the probability of getting two numbers whose product is even?

As we are rolling two dice => Number of cases =  6^2  = 36

We know that for the product of two numbers to be even at least one of them has to be even.

Let's solve the problem using two methods:

Method 1:

Now there are 4 outcomes possible
(Odd, Odd), (Odd, Even), (Even Odd), (Even, Even) and there is an equal chance of each of them happening

=>  P(Product of two outcomes is even) =  P(At least one number is Even) = P((Odd, Even) or (Even Odd) or (Even, Even)) =  \frac{3}{4}

Method 2:

Out of the 36 comes lets eliminate all options in which both the outcomes are odd
Both can be odd in 3*3 (=9 ways), as in the first roll we can get any number out of 1, 3, and 5. And in the second case also we have these 3 choices.

=>  P(Product of two outcomes is even) =  P(At least one number is Even) =  \frac{36 - 9}{36}  =  \frac{27}{36}  =  \frac{3}{4}

So,  Answer will be B 
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

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Two dice are thrown simultaneously. What is the probability of getting

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