Suppose you roll two fair, six-sided dice - one red and one green. The following figure shows the sample space of this chance process. Are the events "sum is 8" and "green die shows a 4" independent? Justify your answer. P(sum of 8) = 3 = 0.1398 and P(sum of 8 | green is 4) = = 0.1667 36 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent. OP(sum of 8) == 0.1667 and P(sum of 8 | green is 4) = = = 0.1667 6 Because these two probabilities are equal, the events "sum is 8" and "green die shows a 4" are independent. P(sum of 8) == 0.1398 and P(sum of 8 | green is 4) = = = 0.2 36 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent. P(sum of 8) = 36 = 0.1398 and P(sum of 8 | green is 4) == 0.1667 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are independent. P(sum of 8 and green is 4) = 3 = 0.278 and P(sum of 8 and not green is 4) = 3 = 0.111 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent.
Suppose you roll two fair, six-sided dice - one red and one green. The following figure shows the sample space of this chance process. Are the events "sum is 8" and "green die shows a 4" independent? Justify your answer. P(sum of 8) = 3 = 0.1398 and P(sum of 8 | green is 4) = = 0.1667 36 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent. OP(sum of 8) == 0.1667 and P(sum of 8 | green is 4) = = = 0.1667 6 Because these two probabilities are equal, the events "sum is 8" and "green die shows a 4" are independent. P(sum of 8) == 0.1398 and P(sum of 8 | green is 4) = = = 0.2 36 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent. P(sum of 8) = 36 = 0.1398 and P(sum of 8 | green is 4) == 0.1667 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are independent. P(sum of 8 and green is 4) = 3 = 0.278 and P(sum of 8 and not green is 4) = 3 = 0.111 Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Suppose you roll two fair, six-sided dice - one red and one green. The following figure shows the sample space of this chance
process.
Are the events "sum is 8" and "green die shows a 4" independent? Justify your answer.
P(sum of 8) = 3 = 0.1398 and P(sum of 8 | green is 4) = = 0.1667
36
Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent.
OP(sum of 8) == 0.1667 and P(sum of 8 | green is 4) = = = 0.1667
6
Because these two probabilities are equal, the events "sum is 8" and "green die shows a 4" are independent.
P(sum of 8) == 0.1398 and P(sum of 8 | green is 4) = = = 0.2
36
Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent.
P(sum of 8) = 36 = 0.1398 and P(sum of 8 | green is 4) == 0.1667
Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are independent.
P(sum of 8 and green is 4) = 3 = 0.278 and P(sum of 8 and not green is 4) = 3 = 0.111
Because these two probabilities are not equal, the events "sum is 8" and "green die shows a 4" are not independent.
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