When the two six-sided fair dice are rolled then we get total of 36 order pairs.
In the first question,
in which we have to find the probability that at least one number is odd and the sum of two numbers is even; for this question we get the total of 9 order pairs which are (1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)
Probability= no. of order pairs that contain at least one number is odd and the sum of two numbers is even) / total no. of order pairs
P= 9/36
P=1/4
For the second question,
four order pairs which will fulfill the condition that exactly one number is 6 and the product of the two numbers is at most 15 are (1,6),(2,6),(6,1),(6,2)
So,
Probability= no. of order pairs that exactly one number is 6 and the product of the two numbers is at most 15/ total no. of order pairs
Probability= 4/36
P=1/9
