Imagine you are in a game show There are 4 prizes hidden on

Imagine you are in a game show. There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are worth $1000. You have to pay $50 to the host if your choice is not correct. Let the random variable x be the winning.

(2 pts) Complete the following probability distribution. (Show the probability in fraction format and explain your work)

x

P(x)

-$50

$1,000

$1,500

$4,000

(2 pts) What is your expected winning in this game? (Show work and round the answer to two decimal places)

(2 pts) What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)

Solution

  I\'m assuming you only get ONE pick - is that correct?

If so, the way you calculate the expectation value is to add up all the prizes, times the probability of winning that prize:

E(x) = $4000 * 1/16 + $1500 * 1/16 + $1000 * 2/6 + (-$50) * 12/16
E(x) = $6900/16 = $431.25

b) This is NOT a trivial decision. Yes - you have a higher expectation value by playing the game, but there\'s also a high level of risk - your most likely result is to lose $50. Personally I would take the $400, because the extra $31.25 isn\'t worth the risk.