Having probs with financial expectations...Please help!!! (1 Viewer)

[_manda_87_]

Heya ive been goin through sum of the prac papers and doin the online board of studies mult. choice test and got stuck with this question.....

Amy buys a $1 ticket in a raffle. There are 200 tickets in the raffle and two prizes. First prize is $100 and second prize is $50.

Find Amy's financial expectation.
a) -$1.00
b) -$0.75
c) -$0.25
d) +$0.25

My tutor and i couldnt work it out.If u can do it can u give me the workin out for it as well?
thanks

 

[mojako]

it's c

(needed to download the syllabus to work out what financial expectation is haha... i dont do general.. and needed to work backwards as well)

if you get first prize, you gain $99 ($100 prize - $1 to pay the ticket)
if you get second prize, you get $49
if you don't get the prize, you lose $1

financial expectation:
(for first prize) + (for second prize) + (for no prize)
= 1/200 * 99 + 1/200 * 49 - 198/200 * 1

 

[PC]

First of all work out the probability of the different things that can happen.
P(1st prize) = 1/200
P(2nd prize) = 199/200 x 1/199 = 1/200
P(no prizes) = 199/200 x 198/199 = 99/100
She can't win both prizes as she only has 1 ticket.

Then multiply the probability by the prize...
1st prize: 1/200 x $100 = $0.50
2nd prize: 1/200 x $50 = $0.25
No prizes; 99/100 x $0 = $0

Add all these amounts together: 0.50 + 0.25 + 0 = $0.75

BUT it costs $1 to enter.
Therefore expectation = 0.75 - 1 = -$0.25

So answer is C

Hope this helps

Good luck on Tuesday

 

[moose87]

ok ok ok ....rewind...
i dont get the whole concept of F.Expctn...
NOT ONE LIL BIT!!!!
how do u figure out whether the amounts are added together or subtracted....AHHHH i hope there isnt one of these lil shits in the exam :|
does it make sense that i understand the final part *shaking head* i get everything but this....grrr

 

[PC]

In that question there were just prizes (win $100 for first, win $50 for second), so all amounts were positive or zero. So you just add them all up.
BUT
there was a $1 entry free, which you lose when you enter, so you need to subtract then.

Look at last year's HSC (Q27b)
Two unbiased dice are thrown. The dice each have six faces. The faces are numbered 1,2,3,4,5 and 6.
Dale plays a game with these dice. There is no entry fee.
When the dice are thrown:
• Dale wins $20 if both dice show a 6.
• He wins $2 if there is only one 6.
• He loses $2 if neither shows a 6.
What is his financial expectation from this game?

First work out the probability for all the dot points...
P(both 6) = 1/36
P(only one 6) = 10/36
P(no 6) = 25/36

Then multiply by the prizes:
Both 6: 1/36 x $20 = 5/9 .... (don't round off yet)
One 6: 10/36 x $2 = 5/9
No 6s: 25/36 x -$2 = -1 7/18 .... (this one's negative because you lose!)

Add these all together:
5/9 + 5/9 - 1 7/18 = -5/18 = -$0.28

What this means is that if Dale continues to play this game for an indefinite period then he will lose an average of 28¢ per game.

Does this help?

All the best for tomorrow!

 

[moose87]

ta PC ur a legend....*hugs*...
thanks for the goodluck - fingers crossed they go easy on us...
ta again

 

[notnownotever]

its d
1/200 * 100 - 1/199 *50
=0.25