Question 1197843: A lottery has a $ 2 000 000 first prize, a $ 250 000 second prize, and a three $5000 third prizes. A total of 1 000 000 tickets are sold.
a) What is the probability of winning a prize in this lottery?
b) If a ticket costs $5.00, what is the expected profit per ticket?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Part (a)
m = 1 first place prize
n = 1 second place prize
p = 3 third place prizes
m+n+p = 1+1+3 = 5 prizes total
This is out of 1,000,000 (one million) tickets sold.
The probability of winning a prize is 5/(1,000,000) = 1/(200,000) or "1 out of 200,000".
Answer as a fraction: 1/200000
Answer as a decimal: 0.000005
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Part (b)
| Scenario | Probability as a fraction | Probability as a decimal | | Win 1st prize | 1/(1,000,000) | 0.000001 | | Win 2nd prize | 1/(1,000,000) | 0.000001 | | Win 3rd prize | 3/(1,000,000) | 0.000003 | | Don't win anything | (999,995)/(1,000,000) | 0.999995 |
The decimal values are exact without any rounding done to them.
X = net winnings aka profit
If a ticket costs $5, then we have these possible profits
$2,000,000 - $5 = $1,999,995
$250,000 - $5 = $249,995
$5,000 - $5 = $4,995
0-5 = -5 dollars
List each X with its corresponding P(X) value. I'll go with the decimal form of P(X).
| X | P(X) | | 1,999,995 | 0.000001 | | 249,995 | 0.000001 | | 4995 | 0.000003 | | -5 | 0.999995 |
Multiply each X value with its corresponding probability to form the X*P(X) column.
| X | P(X) | X*P(X) | | 1999995 | 0.000001 | 1.999995 | | 249995 | 0.000001 | 0.249995 | | 4995 | 0.000003 | 0.014985 | | -5 | 0.999995 | -4.999975 |
Add up the items in the X*P(X) column to get
1.999995 + 0.249995 + 0.014985 + (-4.999975) = -2.735
This rounds to -2.74
With reference to the person who bought the lottery ticket, their expected profit per ticket is -2.74 dollars. They expect to lose, on average, about $2.74 per ticket.
Answer: -2.74 dollars
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
A lottery has a $ 2 000 000 first prize, a $ 250 000 second prize, and a three $5000 third prizes.
A total of 1 000 000 tickets are sold.
a) What is the probability of winning a prize in this lottery?
b) If a ticket costs $5.00, what is the expected profit per ticket?
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As you formulate your problem, I see that you are a beginner in composing Math problems.
I say it because question (a) in the problem is posed incorrectly.
The correct formulation is
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| (a) What is the probability of winning a prize |
| in this lottery, having only one ticket ? |
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