MATH SOLVE

2 months ago

Q:
# In a raffle where 2000 tickets are sold for $2 each, one first prize of $400 and one second prize of $200 will be awarded. What is the expected value of a single ticket in the raffle? Round your answer to the nearest hundredth, and do not include a $ sign or the word "dollars" in your response.

Accepted Solution

A:

Answer:The expected value is -$1.7Step-by-step explanation:Consider the provided information.In a raffle where 2000 tickets are sold for $2 each, One first prize of $400 and one second prize of $200 will be awarded.Suppose you bought a ticket for $2 and win first price, Then the gain will be: $400-$2=$398Suppose you bought a ticket for $2 and win second prize, then the gain will be:$200-$2=$198Suppose you bought a ticket for $2 and you got nothing, the the loss will be -$2.The probability of getting first prize is: [tex]\frac{1}{2000}[/tex]Because only one person is selected for first prize out of 2000.The probability of getting second prize is: [tex]\frac{1}{2000}[/tex]The probability of getting nothing is: Β [tex]\frac{1998}{2000}[/tex]Hence the expected value is:[tex]398\times \frac{1}{2000}+198\times \frac{1}{2000}-2\times \frac{1998}{2000}=-1.7[/tex]Hence, the expected value is -$1.7