Two fair dice are thrown,what is the probability of getting two odd numbers?

1 Answer
KillerBunny
Jun 28, 2018

#1/4#

Explanation:

The two dice are independent, i.e. the result of one die does not infuence the result of the other.

In this case, the probability of a complex event is the product of the probabilities of the simple events.

For every die, there are #3# odd outcomes and #3# even outcomes. So, the probability of getting an odd number is #3/6=1/2#

So, the probability that this happens with both dice is #1/2*1/2=1/4#

In this case, it is actually easy to enumerate the "good" outcomes: there are #36# outcomes in total (all numbers from #1# to #6# for one die and the same for the other die). The good outcomes are

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

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

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

And in fact, #9# good outcomes over #36# total outcomes means

#9/36 = 1/4#

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