Question

Two six-sided fair dice are rolled.

The probability that at least one number is odd and the sum of the two numbers is even is
v . The probability that exactly one
number is 6 and the product of the two numbers is at most 15 is

Answer 1

Explanation:

There are 36 equally likely pairs: (1,1);(1,2);(1,3),…(6,4);(6,5);(6,6). The corresponding sums: 2,3,4,….10,11,12. are best observed with an addition table for 1-6 with 1-6. 3 is simple enough because only (1,2) and (2,1) can sum to 3. So P= 2/36 = 1/18. P(SUM =4) = 3/36 because (1,3);(2,2);(3,1) are the only pairs that sum to 4. The best way to see this is look at the first die. To get a sum of 4, the first die must be 1,2 or 3. Each of those first rolls forces one outcome for the second die. P(10) = 3/36 because the first die must be 4,5,or6.