i need help with this one. And please explain the works?

I assume each cube has faces numbered 1 to 6, as a die.

(a) The sum is even only if both dice come up even or both come up odd. The probability is 2/4, in other words, ½ or 50%, because there are 4 possible outcomes: even/even (even sum), even/odd (odd sum), odd/even (odd sum), odd/odd (even sum). And there are as many odd numbers on a die as even. However, if the numbers are descending it means one is bigger than the other so we can't have two numbers the same. There are 36 outcomes when rolling two dice, so 18 have an even sum. But in 6 of these, the dice show the same number, which leaves 12 with even sum and different numbers. So the probability is 12/36=⅓ or 33⅓%.

(b) As we've seen in (a), the probability of an odd sum is ½ or 50%.

(c) If one die shows 1 then the other die can have any value, so we have 6 sums no greater than 7.

If a die shows 2 then only the sum of 5 values will be no greater than 7.

So we have out of 36 possible outcomes 6+5+4+3+2+1=21 sums no greater than 7.

That's a probability of 21/36=7/12 or 58⅓%.

by Top Rated User (1.1m points)