Respuesta :
The expected sum of the numbers that appear on two dice is = 10
Each die has 6 possible values, so a pair of dice have a total of 6*6=36 outcomes.
To find a sum of 10, the cases are:
(4,6), (5,5) and (6,4).
So to have a sum of 10 we have 3 cases among the 36 possible, therefore the probability is:
P(10) = 3/36 = 1/12
If we want the sum of 10 in each of the three rolls, the probability is:
P(10 on three rolls) = P(10)^3 = (1/12)^3 = 1/1728 = 0.0005787
If the sum is 10 in two of three rolls, in one roll we need the probability of the sum not being 10:
P(not 10) = 1 - P(10) = 1 - (1/12) = 11/12
So we have:
P(10 in two of three rolls) = P(10)^2 * P(not 10) = (1/12)^2 * (11/12)
P(10 in two of three rolls) = 11/1728 = 0.0063657
A={(3,6),(4,5),(5,4),(6,3),(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
There are 10 possible outcomes of two dices under the condition.
To find the expected value of conditional probability. We need to multiply the possibility with the summed value of two dices:
E(X|A)=(4*9/10)+(3*10/10)+(2*11/10)+12/10=10
Therefore,
The expected sum of the numbers that appear on two dice is = 10
To learn more about Dice problems visit :
brainly.com/question/14255954
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