The island club... ten thousand tickets sold for $2 each... first prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each, and 20 consolation of $100 each. Find the expected value.
Is it found through
(1/10k) * (3000) + (3/10k) * (1000) + (5/10k) *(500) + (20/10k) * (100)?
yes
Yes, you are on the right track. The expected value can be found using the formula:
(expected value) = (probability of event 1) * (value of event 1) + (probability of event 2) * (value of event 2) + ... + (probability of event n) * (value of event n)
In this case, the events are the different prizes and their corresponding probabilities and values:
Event 1: First prize of $3000
Event 2: three second prizes of $1000 each
Event 3: five third prizes of $500 each
Event 4: twenty consolation prizes of $100 each
To calculate the expected value, we need to calculate the probabilities of each event occurring and multiply them by their corresponding values.
Assuming all tickets have an equal chance of winning, the probabilities can be calculated as follows:
Probability of event 1 = (Number of first prize winners) / (Total number of tickets sold) = 1 / 10000
Probability of event 2 = (Number of second prize winners) / (Total number of tickets sold) = 3 / 10000
Probability of event 3 = (Number of third prize winners) / (Total number of tickets sold) = 5 / 10000
Probability of event 4 = (Number of consolation prize winners) / (Total number of tickets sold) = 20 / 10000
Now, we can substitute these probabilities and the values of each event into the formula:
(expected value) = (1 / 10000) * 3000 + (3 / 10000) * 1000 + (5 / 10000) * 500 + (20 / 10000) * 100
After calculating this expression, you'll get the expected value of the island club tickets.