Answer:
The expected sum of the numbers on the upward faces of the two dice is 7.
Step-by-step explanation:
Consider the provided information.
If two pair of dice tossed the possible out comes are:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6,6)
Now we need to find the expected sum of the numbers on the upward faces of the two dice.
The expected sums can be:
Sum: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Prob: 1/36, 2/36, 3/36, 4/36, 5/36, 6/36, 5/36, 4/36, 3/36, 2/36, 1/36
As we know that the expectation of experiment can be calculated as:
[tex]P(S_1)\cdot S_1+P(S_2)\cdot S_2+........+P(S_n)\cdot S_n[/tex]
Here S represents the numerical outcomes and P(S) is the respective probability.
Substitute the respective values in the above formula.
[tex]=2\times\frac{1}{36}+3\times\frac{2}{36}+4\times\frac{3}{36}+5\times\frac{4}{36}+6\times\frac{5}{36}+7\times\frac{6}{36}+8\times\frac{5}{36}+9\times\frac{4}{36}+10\times\frac{3}{36}+11\times\frac{2}{36}+12\times\frac{1}{36}\\=\frac{252}{36}\\=7[/tex]
Hence, the expected sum of the numbers on the upward faces of the two dice is 7.
The expected sum of the numbers on the upward faces of the two dice is 7
The expected value is defined thus :
Sample space for 2 die rolls = 6² = 36
The total possible sum include :
Value(X) _ Frequency___p(X)
2 ______1 _________ 1/36
3 ______2 _________ 2/36
4 ______3 _________ 3/36
5 ______4 _________ 4/36
6 ______5 _________ 5/36
7 ______ 6 _________ 6/36
8 ______ 5 _________ 5/36
9 ______ 4 _________ 4/36
10 _____ 3 __________3/36
11 ______ 2 _________ 2/36
12 ______ 1 _________ 1/36
The Expected value :
E(X) = 2(1/36)+3(2/36)+4(3/36)+5(4/36)+6(5/36)+7(6/36)+8(5/36)+9(4/36)+10(3/36)+11(2/36)+12(1/36)
E(X) = 1/18+1/6+1/3+5/9+5/6+7/6+10/9+1+5/6+11/18+1/3
E(X) = 7
Therefore, the expected value of the toss is 7
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