Question

Each of a, b, c, and d has a value chosen independently, with equal probability 1/10, from 0,1,2,3,4,5,6,7,8,9. The values chosen need not be different. What is the probability that ab+cd is odd?

Answer 1

To find the probability that ab+cd is odd, we need to consider the possible combinations of values for a, b, c, and d. If a and b are both odd or both even, their sum will be even. Similarly, if c and d are both odd or both even, their sum will be even. Therefore, to get an odd sum, either a and b must be odd while c and d are even, or a and b must be even while c and d are odd. The probability that ab+cd is odd is 1/4.

Step-by-step explanation:

To find the probability that ab+cd is odd, we need to consider the possible combinations of values for a, b, c, and d.

If a and b are both odd or both even, their sum will be even. Similarly, if c and d are both odd or both even, their sum will be even.

Therefore, to get an odd sum, either a and b must be odd while c and d are even, or a and b must be even while c and d are odd.

Since each value has an equal probability of 1/10, the probability of selecting an odd value for a or b is 5/10 and the probability of selecting an even value for c or d is also 5/10.

So the probability that ab+cd is odd is (5/10) * (5/10) = 1/4.