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 (i. e., are A and B independent events, are A and C independent, and are B and C independent) ? Yes, the events are pairwise independent. No, one pair is not independent. No, two pairs are not independent. No, none of the pairs are independent. Are the three events mutually independent? Yes, the three events are mutually independent. No, the three events are not mutually independent.

Question

Mathematics

Quentin

24 August, 21:14

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 (i. e., are A and B independent events, are A and C independent, and are B and C independent) ? Yes, the events are pairwise independent. No, one pair is not independent. No, two pairs are not independent. No, none of the pairs are independent. Are the three events mutually independent? Yes, the three events are mutually independent. No, the three events are not mutually independent.

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Answers (1)

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Jeremy Bradshaw · Answer 1

(a). No, two pairs are not independent.

(b). No, the three events are not mutually independent.

Step-by-step explanation:

The events are said to be independent event if occurrence of one event does not affect the other event.

(a) The event A and B are independent to each other, Since occurrence of one event does not affect the other event.

But event (A and C) and event (B and C) are dependent event. Since occurring of event C is depend on the events A and B.

Thus, two pairs are not independent.

(b) Since occurring of event C is depend on the events A and B. Thus, the three events are not mutually independent.