Question

If you roll two fair six sided dice what's the probability that both dice show an odd number

Answer 1

Answer with explanation:

When a die is thrown once, total possible outcome ={1,2,3,4,5,6}=6

Total number of odd number in total possible outcome when a die is thrown once ={1,3,5}=3

Probability of an event

                                $=\frac{\text{Total Possible Outcome}}{\text{Total favorable outcome}}$

Probability of getting an Odd number when a Dice is thrown once

         $=\frac{3}{6}\\\\=\frac{1}{2}$

So, When a two fair six sided dice is rolled, the probability that both dice show an odd number

              $=\frac{1}{2}\times \frac{1}{2}\\\\=\frac{1}{4}$

Answer 2

Answer: $\dfrac{1}{4}$

Step-by-step explanation:

If we roll  two fair six sided dice, then the total number of possible outcomes :-

$6\times6=36$    ( by fundamental principle of counting.)

Total Odd numbers  (1,3,5)= 3  

Favorable outcomes for both dice show an odd number = $3\times3=9$            ( by fundamental principle of counting.)

Now, the  probability that both dice show an odd number :-

$\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{9}{36}=\dfrac{1}{4}$

Hence, the probability that both dice show an odd number $=\dfrac{1}{4}$