Question

I have a probability question. I have attached the document at the bottom. This one requires me to show all work. Thanks everyone!

Answer 1

the formula for expected value of a function X is
\(\sum_{\text{value \(x\) taken by }X} x\times P(X=x)\).
Here you want the expected value of the gain.
Gain can be equal to 0 or 1000. Please try from here.

Answer 2

Oh my goodness! I have't a clue :(

Answer 3

The ticket is worth: 0, or 1000. No other possibility.
This means that the \(x\)'s in the sum will be \(x=0\) and \(x=1000\). Nothing else.

Now we need the probabilities \(P(X=0\) and \(P(X=1000)\). Can you find that?

Answer 4

Is this is still on (a)? I'll try it

Answer 5

-0.994

Answer 6

500 tickets. 1 is worth 1000, 499 are worth 0.
The probability to purchase the winning ticket is 1/500. The probability of purchasing a loosing ticket is 499/500.

Answer 7

Don't you multiply those together?

Answer 8

1/500*499/599 right?

Answer 9

No, the formula is \[\sum_x x \times P(X=x)\]
Here it is \(0 \times P(\text{loosing ticket}) + 1000 \times P(\text{winning ticket})\).

Answer 10

\(0\times \frac{499}{500} + 1000 \times \frac{1}{500} = 0 + 2 = 2\). That is the expected value.

Answer 11

Ok, thank you...I can see that now.....how about for (b)

Answer 12

2 is the expected value if you payed nothing for the ticket

Answer 13

have you already met such a question? ("fair price" linked with the topic of expected value)

Answer 14

*paid

Answer 15

Zarkon, you know this problem well?

Answer 16

Raul paid $3 for a ticket..so his expected value is -3+2=-1

Answer 17

Was my answer of -0.994 wrong for (a)

Answer 18

you can also get that by letting X equal the amount of money Raul wins

with prob 499/500 he 'wins' -$3

with probability 1/500 he wins $997 (1000 minus the 3 he spant on the sicket


so

\[E[X]=-3\frac{499}{500}+997\frac{1}{500}=-1\]

Answer 19

*spent

Answer 20

Ok, how about for b?

Answer 21

A fair price would be when the expected winnings is zero

since the expected value of the ticket is $2 then $2 would be a fair price

Answer 22

Thank you for all of your help! Appreciate it :)