Question

You roll a​ die, winning nothing if the number of spots is even​, ​$3 for a 1 or a 3​, and ​$18 for a 5.

​a) Find the expected value and standard deviation of your prospective winnings.

​b) You play three times. Find the mean and standard deviation of your total winnings. ​

c) You play 30 times. What is the probability that you win at least ​$160​?

Answer 1

Probability of even number= 3/6= 0.5

Probability of 1 or 3= 2/6= 0.3333

Probability of 5= 1/6= 0.1667

X	P(X)	X*P(X)	X2 * P(X)
0	0.5	0	0
3	0.3333	0.9999	2.997
18	0.1667	3.0006	54.0108
Total	1	4.0005	57.0078

a) From the above table,

Expected value,  

b) Let Y=X1+X2+X3

Where Xi is winning amount for the ith game; i=1,2,3

the expected value is given by,

c) Let X be the amount won in the game.

For 30 trials,

Mean= 30*4.0005= 120.0015

From standard normal table, P(z>1.14)=0.1271

Required Probability= 0.1271.

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