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

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Re: What is the probability of rolling two fair dice and having each die [#permalink]
Bunuel wrote:
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

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.

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What is the probability of rolling two fair dice and having each die [#permalink]
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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) = $$\frac{9}{36}$$ = $$\frac{1}{4}$$