A player pays $2 and spins the spinner. If the spinner lands on purple, the play

Question

A player pays $2 and spins the spinner. If the spinner lands on purple, the player wins $0.50. If the spinner lands on yellow, the player wins $5. If the spinner lands on blue, the player wins $1. If the spinner lands on red, the player wins nothing. Is the player expected to win money or lose money? How much is the expected gain/loss? A local club plans to invest $10000 to host a baseball game. They expect to sell tickets worth $15000. But if it rains on the day of game, they won't sell any tickets and the club will lose all the money invested. If the weather forecast for the day of game is 20% possibility of rain, what is the expected value of the gain/loss of the club? What is the variance? List all the ordered pairs in the relation R = {(a, b) | gcd(a, b) = 1} on the set {2, 3. 4. 5. 6}.

Explanation / Answer

Solution:

(4) Since player pays $2 for each spin

therefore cost for each spin = $2

Now

Probability of spinner lands on purple = 2/8

and total weighted price of this purple = (2/8) * 0.5 = $ 1/8

Similerly

Probability of spinner lands on yellow = 2/8

and total weighted price of this yellow = (2/8) * 5 = $ 10/8

similerly

Probability of spinner lands on Blue = 3/8

and total weighted price of this blue = (3/8) * 1 = $ 3/8

similerly

Probability of spinner lands on red = 1/8

and total weighted price of this red = (1/8) * 0 = $ 0

Now

Expected profit = Total price value ( sum of all weighted price ) - Cost

= (1/8 + 10/8 + 3/10 +0 ) - 2

= 14/8 -2

= -2/8

=-1/4

As we can see that profit is in negative that means

Player is expected to lose money

Now

expected loss for each spin = $ 1/4 = $0.25

Answer

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