two standard number cubes are tossed. State whether the events are mutually exclusive.?

Start with a 'working definition' for "mutually exclusive events !"

http://www.mathsisfun.com/data/probability-events-mutually-exclusive.html

1) one of the numbers is 1 less thane the other. the sum is odd.

two consecutive numbers must necessarily be an odd number and an even number. the sum of:

(odd) + (even) = (ODD)

2) The sum is greater than 10. Six is one of the numbers.

What combinations of the dice give a sum greater than 10 (i.e., 11 or 12) ??

(5, 6), (6, 5), (6, 6)

Now, consider the question of "mutually exclusive," now that you have the possible events...You have to try !!

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If the 'number cubes' are dice, the numbers on the different faces are 1, 2, 3, 4, 5, and 6.

If one number is 1 less than the other, the sum MUST be an odd number. Any odd number plus any even number will sum to an odd number. To get two odd numbers or two even numbers (either of which would sum to an even number), the numbers would have to differ by 2, not 1. The conditions set in the question are not mutually exclusive.

If the sum is GREATER than 10, at least one of the numbers HAS to be a six. If you had two fives, the sum does not exceed 10. The conditions set in the question are not mutually exclusive.