In a lottery, 5000 tickets are sold for $1 each.... one1st prize of $2000, 1 2nd prize of $500, 3 third prizes of $100, and 10 consolation prizes of $25 are to be awarded.
I want to set up a probability distribution table to help me solve this problem but I don't know what should go under the x variable and p (x=x).
P(x=v) = (# prizes worth $v)/(total # prizes)
I attempted to find the E(X) and got .61 (1/5000)*(2000)+(1/5000)*(500)+(3/5000)*(100)+(10/5000)*(25).
To set up a probability distribution table, we need to determine the different possible outcomes, assign them to the x variable, and calculate their corresponding probabilities (p(x)).
In this scenario, the possible outcomes are winning the different prizes. Let's assign the following outcomes to the x variable:
x = 1st prize
x = 2nd prize
x = 3rd prize
x = consolation prize
x = no prize
Now, we need to calculate the probabilities for each outcome:
1. Probability of winning the 1st prize: Since there is only one 1st prize, the probability of winning is 1/5000.
p(x = 1st prize) = 1/5000
2. Probability of winning the 2nd prize: Since there is only one 2nd prize, the probability of winning is 1/5000.
p(x = 2nd prize) = 1/5000
3. Probability of winning a 3rd prize: There are three 3rd prizes, so the probability of winning one is 3/5000.
p(x = 3rd prize) = 3/5000
4. Probability of winning a consolation prize: There are ten consolation prizes, so the probability of winning one is 10/5000.
p(x = consolation prize) = 10/5000
5. Probability of not winning any prize: The remaining outcomes are not winning any prize, which means the probability of not winning any prize is 1 minus the sum of the probabilities for all the other outcomes.
p(x = no prize) = 1 - (p(x = 1st prize) + p(x = 2nd prize) + p(x = 3rd prize) + p(x = consolation prize))
Once you calculate the above probabilities, you can create a probability distribution table with the x variable and their corresponding probabilities (p(x)).