A lottery offers one $10000 prize, one $5000 prize and five $1000 prizes. 1000 tickets are sold at $30 each . Find the expectation if a person buys one ticket
workings:
9970/1000+4970/1000+4850/1000-29790/1000
= -10000/1000 =-$10
correct baba gurl UWUWUWUWUWUW
To find the expectation, you need to multiply each outcome by its probability and then sum them up. Let's go step by step:
1. Calculate the expected value for winning the $10,000 prize:
Probability of winning the $10,000 prize = 1/1000 (only one winner out of 1000 tickets)
Expected value of winning the $10,000 prize = (1/1000) * $10,000 = $10
2. Calculate the expected value for winning the $5,000 prize:
Probability of winning the $5,000 prize = 1/1000 (only one winner out of 1000 tickets)
Expected value of winning the $5,000 prize = (1/1000) * $5,000 = $5
3. Calculate the expected value for winning one of the five $1,000 prizes:
Probability of winning a $1,000 prize = 5/1000 (five winners out of 1000 tickets)
Expected value of winning a $1,000 prize = (5/1000) * $1,000 = $5
4. Calculate the expected value for not winning any of the above prizes (losing):
Probability of not winning any prize = 993/1000 (993 tickets that didn't win any prize)
Expected value of not winning any prize = (993/1000) * $0 = $0
Now, sum up all the expected values:
Expected value = $10 + $5 + $5 + $0
Expected value = $20
Therefore, the expected value if a person buys one ticket is $20.