Question

In: Statistics and Probability

Create the probability distribution in a table for all the outcomes where X is the random...

Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded. (already done)
Communicate how you arrived at the probability of each outcome.
What is the expected value, E(X), for the game? You may include this in your table from the distribution. If the game costs 10 points to play, how much would the player expect to win or lose?

Three Prize roller

Outcome	x	P(x)	xP(X)
1	0
2	10
3	0
4	20
5	0
6	28
		TOTAL

Word scramble

a)

Outcome	x	P(x)	xP(X)
Just 1st	0
Just 2nd	5
Just 3rd	15
Just 4	10
2 letter with 1st	20
2 letter without 1st	25
All 4	40
No letter	0
		Total

Ten spinner

Outcomes - greens	x	P(x)	xP(X)
0	15
1	10
2	0
3	0
4	5
5	20
6	50
7	70
8	500
9	10000
10	100000
		Total

Expert Solution

Three Prize roller

Outcome	x	P(x)	xP(X)
1	0	0	0
2	10	0.172414	1.724138
3	0	0	0
4	20	0.344828	6.896552
5	0	0	0
6	28	0.482759	13.51724
Total	58	1	22.13793

Expected value = 22.13793

Player will win = 22.13793 - 10 = 12.13793

===============================================

Outcome	x	P(x)	xP(X)
Just 1st	0	0	0
Just 2nd	5	0.043478	0.217391
Just 3rd	15	0.130435	1.956522
Just 4	10	0.086957	0.869565
2 letter with 1st	20	0.173913	3.478261
2 letter without 1st	25	0.217391	5.434783
All 4	40	0.347826	13.91304
No letter	0	0	0
Total	115	1	25.86957

Expected value = 25.86957

Expected win = 15.86957

=========================================================

Ten spinner

Outcomes - greens	x	P(x)	xP(X)
0	15	0.00013554	0.00203307
1	10	9.0359E-05	0.00090359
2	0	0	0
3	0	0	0
4	5	4.5179E-05	0.0002259
5	20	0.00018072	0.00361435
6	50	0.00045179	0.02258968
7	70	0.00063251	0.04427577
8	500	0.00451794	2.2589681
9	10000	0.09035872	903.587241
10	100000	0.90358724	90358.7241
Total	110670	1	91264.644

Expected value = 91264.644

orchestra answered 1 year ago

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