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there are two baskets, in the first, 4 red , 8 white balls, in the second 7 red and 6 white balls, two balls are taken from each baskets. the outcome of which of the two experiments, should be considered more uncertain

there are two baskets, in the first, 4 red , 8 white balls, in the second 7 red and 6 white balls, two balls are taken from each baskets. the outcome of which of the two experiments, should be considered more uncertain

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 27E: Another friend asks you to explain how to tell whether two events are dependent or independent. How...
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there are two baskets, in the first, 4 red , 8 white balls, in the second 7 red and 6 white balls, two balls are taken from each baskets. the outcome of which of the two experiments, should be considered more uncertain?

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there are two baskets, in the first, 4 red , 8 white balls, in the second 7 red and 6 white balls, two balls are taken from each baskets. the outcome of which of the two experiments, should be considered more uncertain?

*can I the solution of this question same like the example in the picture

Example 4. There are two baskets. In the first - 5 red, 7 white balls. In the second - 8 red and 6 white balls. Two balls are taken from each baskets. The outcome of which of the two experiments should be considered more uncertain? Solution. Consider the first experiment, drawing two balls from the first urn, as a system X with three outcomes: исходы х X1 X2 23 (2 кр.ш.) (1 кр.п.+1 бел.ш.) | (2 бел.ш.) вероятности исходов | i i =iii+h n = wit=1 Найдем энтропию системы Х 132 = 11 n() + n() + n() 0,4118 +0,4854 +0,5256 = H(X) 1, 4228 бит = 132 Consider the second experiment, drawing two balls from the second basket, as a system Y with three outcomes: исходы уз у (2 кр.ш.) (1 кр.ш.+1 бел.ш.) (2 бел.ш.) вероятности исходов Let's find the entropy of the system Y: H(Y) = n (i) + n (1) + 7 (9) = 0,5230 +0,4870 +0,4277 1, 4377 бит. Because H(X) <H(Y), then the outcome of the second experiment is more uncertain
Transcribed Image Text:Example 4. There are two baskets. In the first - 5 red, 7 white balls. In the second - 8 red and 6 white balls. Two balls are taken from each baskets. The outcome of which of the two experiments should be considered more uncertain? Solution. Consider the first experiment, drawing two balls from the first urn, as a system X with three outcomes: исходы х X1 X2 23 (2 кр.ш.) (1 кр.п.+1 бел.ш.) | (2 бел.ш.) вероятности исходов | i i =iii+h n = wit=1 Найдем энтропию системы Х 132 = 11 n() + n() + n() 0,4118 +0,4854 +0,5256 = H(X) 1, 4228 бит = 132 Consider the second experiment, drawing two balls from the second basket, as a system Y with three outcomes: исходы уз у (2 кр.ш.) (1 кр.ш.+1 бел.ш.) (2 бел.ш.) вероятности исходов Let's find the entropy of the system Y: H(Y) = n (i) + n (1) + 7 (9) = 0,5230 +0,4870 +0,4277 1, 4377 бит. Because H(X) <H(Y), then the outcome of the second experiment is more uncertain
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