Consider independently rolling two fair dice, one red and the other green. Let A

Question

Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die shows 3 dots, B be the event that the green die shows 4 dots, and C be the event that the total number of dots showing on the two dice is 7. Are these events pairwise independent (.e, are A and B independent events, are A and C independent, and are 8 and C independent)? O Yes, the events are pairwise independent No, one pair is not independent. O No, two pairs are not independent. ONo, none of the pairs are independent. O Yes, the three events are mutually independent. O No, the three events are not mutually independent.

Explanation / Answer

A and B are independent since number appearing on the red die is independent of the number appearing on the green die when two dices are rolled independently.

A and C are dependent since the number appearing on the Red die sums up to the total sum of the numbers obtained on the two dices.

Similarly, B and C are dependent.

Hence, only two pairs are not independent.

A, B and C are mutually dependent since event C is nothing but the outcome of the numbers on red and green dices which represent event A and B respectively.

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