Question

Roll a pair of fair dice. Let X be the number of ones in the outcome and let Y be the number of twos in the outcome. Are X and Y independent?

Answer 1

Here X and Y are dependent events

Because , on rolling two dices, there can be 4 cases as following type

1. Outcome of one dice is 1
2. Outcome of both dice is 1
3. Outcome of one dice is 2
4. Outcome of both dice is 2

In case 1 and case 4 ,we can easily see that , if outcome of any dice is 1 .then both outcome can not be 2

Similarly in case 2,3 we can see that if outcome of any dice is 2 than both dice can not be 1

From above explanation we can conclude that events depends on each other .

Hence we can conclude that events X and Y are dependent events.

Please like??