A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine...

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine the probability distribution for the sum of the two dice. Create a frequency histogram for the probability distribution and determine the expected sum of the two dice.

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Expert Solution

Solution:-

The probability distribution for the sum of the two dice.

Sum(x)	Frequency	P(x)
2	1	0.020833
3	2	0.041667
4	3	0.0625
5	4	0.083333
6	5	0.104167
7	6	0.125
8	6	0.125
9	6	0.125
10	5	0.104167
11	4	0.083333
12	3	0.0625
13	2	0.041667
14	1	0.020833
Sum	48	1

The frequency histogram for the probability distribution is

The expected sum of two dices is 8

Sum(x)	Frequency	P(x)	x*P(x)
2	1	0.020833	0.041667
3	2	0.041667	0.125
4	3	0.0625	0.25
5	4	0.083333	0.416667
6	5	0.104167	0.625
7	6	0.125	0.875
8	6	0.125	1
9	6	0.125	1.125
10	5	0.104167	1.041667
11	4	0.083333	0.916667
12	3	0.0625	0.75
13	2	0.041667	0.541667
14	1	0.020833	0.291667
Sum	48	1	8

E(x) = x*P(x)

E(x) = 8

orchestra answered 10 months ago

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