a) The highest value of P(x) is 0.208 for when X=$300. Hence that is the most likely dollar amount that can be won.
ans: The most likely dollar amount is $300
b) When you spin Lose a turn or Bankrupt, the amount won is x=$0. The probability value P(x) for x=0 is 0.083.
ans: The probability to spin Lose a turn or Bankrupt is 0.083
c) the average dollar amount is the expected value of X. It is calculated as below
The average dollar amount is $668.75
d) The probability that the contestant spins $0 in any given turn is P(x=0)=0.083
the probability that the contestant spin $0 each time is
(Probability that spin $0 first time)x(Probability that spin $0 second time)x(Probability that spin $0 third time) =
P(X=0)xP(X=0)xP(X=0) = 0.083*0.083*0.083 = 0.0006.
We can also solve this using a Binomial distribution as given below.
Let Y be the number of times the contestant spins $0 out of 3 spins. We can say that y has a Binomial distribution with parameters, number of trials n=3 and the success probability p=0.083.
The probability of spinning $0, Y=y number of times is given by (the Binomial probability is)
The probability that the contestant spin $0, 3 out of 3 times is given by the probability of Y=3
ans: The probability that the contestant spin $0, 3 out of 3 times is 0.0006
e) The probability that the contestant spins $0 at least one time out of 3 is same as 1- (probability that the contestant does not spin $0 each of 3 times)
The probability that the contestant does not spin $0 in any given turn is 1-P(x=0)=(1-0.083) = 0.917
the probability that the contestant spin does not $0 each of 3 times is
(Probability that does not spin $0 first time)x(Probability that does not spin $0 second time)x(Probability that does not spin $0 third time) =(1-P(X=0))x(1-P(X=0))x(1-P(X=0)) = 0.917*0.917*0.917 = 0.7703
The probability that the contestant spins $0 at least one time out of 3 is same as 1- (probability that the contestant does not spin $0 all 3 times) = 1-0.7703=0.2297
Alternatively, we can use Binomial distribution.
The probability that the contestant spin $0 at least one time out of 3 is same as the probability that Y is 1 or more
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