What is the probability of rolling two fair dice and having each die

Question

What is the probability of rolling two fair dice and having each die show an odd number?

A. 1/6
B. 1/4
C. 1/2
D. 3/4
E. 35/36

vitaliyGMAT · Answer

We have independent events, the outcome of one event does not influence the outcome of the other.

P (odd in die #1) * P(odd in die #2) = 1/2 * 1/2 = 1/4

Answer B

BrentGMATPrepNow · Answer

Each die has six possible outcomes: 1, 2, 3, 4, 5, or 6 
Three of those outcomes are odd (1, 3 and 5). 
So, P(a die is odd) = 3/6 =  1/2

P(both are odd) = P(1st die is odd   AND   2nd die is odd)
= P(1st die is odd)   x   P(2nd die is odd)
=  1/2    x    1/2 
= 1/4

Answer: B

Cheers, 
Brent

ScottTargetTestPrep · Answer

There are 3 odd and 3 even outcomes on a single die, so the probability of rolling an odd number on 1 die is 3/6 = 1/2. Because we want two dice to each show an odd number, we multiply the probabilities. Thus, the probability that each die shows an odd number is 3/6 x 3/6 = 1/2 x 1/2 = 1/4.

Answer: B

BrushMyQuant · Answer

We need to find What is the probability of rolling two fair dice and having each die show an odd number?

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

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(Both will be odd) =  \frac{1}{4}

Method 2:

Both the die 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.

(1,1), (1,3), (1,5)
(3,1), (3,3), (3,5)
(5,1), (5,3), (5,5)

=> P(each die show an odd number) =  \frac{9}{36}  =  \frac{1}{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

What is the probability of rolling two fair dice and having each die

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