S1 Little Problem

Sorry if this is a little annoying, I have worked it out but the answer on the bottom is different. Could you please show your working so I can see where I have gone wrong.

5. A fruit machine consists of three windows, each of which shows pictures of fruits - lemons, oranges, cherries or plums. The probability that a window shows a particular fruit is as follows:

P(lemons) = 0.4, P(oranges) = 0.1, P(cherries) = 0.2, P(plums) = 0.3

The windows operate independently. Anyone wanting to play the machine pays 10p for a turn.
The winning combinations are as follows:

Oranges in 3 windows £1.00
Cherries in 3 windows £0.50
Oranges in 2 windows and cherries in 1 window £0.80
Lemons in 3 windows £0.40

Complete the table below:

Winning Combination 3 oranges 3 cherries 2 oranges/1 cherry 3 lemons Lose
Winnings 90p 40p 70p 30p -10p
Probability 0.001 0.001 0.008 0.064 0.921

Find the expected gain or loss per turn. Find the standard deviation.

P.S. ive added an attatchment as its not to clear

OP

Does nobody know how to do this? Its only a simle decrete random variable.

Reply 2

Dekota

shrek

Winnings 90p 40p 70p 30p -10p
Probability 0.001 0.001 0.008 0.064 0.921

... [90(0.001) + 40(0.001) + 70(0.008) + 30(0.064) -10(0.921)] = -6.6p

E(X) = -6.6p

I'm not sure if thats right, so won't work out SD, but I know who can work this out ... lets wait for her ... :wink:

Reply 3

shrek

OP

1

Ricki

... [90(0.001) + 40(0.001) + 70(0.008) + 30(0.064) -10(0.921)] = -6.6p

E(X) = -6.6p

I'm not sure if thats right, so won't work out SD, but I know who can work this out ... lets wait for her ... :wink:

This is what I got. Its the SD that confused me a bit. This is what I did:

[90^2*0.001) + 40^2(0.001) + 70^2(0.008) + 30^2(0.064) -10^2(0.921)]
=15.8

therefore 15.8-(-6.6^2)= 59.36

SD = sq rt 59.36 = 7.7

but it should be 12.6

Reply 4

evariste_3086

1

shrek

This is what I got. Its the SD that confused me a bit. This is what I did:

[90^2*0.001) + 40^2(0.001) + 70^2(0.008) + 30^2(0.064) -10^2(0.921)]
=15.8

therefore 15.8-(-6.6^2)= 59.36

SD = sq rt 59.36 = 7.7

but it should be 12.6

should it be
[90^2*0.001) + 40^2(0.001) + 70^2(0.008) + 30^2(0.064) +10^2(0.921)]
=200
SD=rt(200-43.56)
=12.507

Reply 5

Dekota

evariste

should it be
[90^2*0.001) + 40^2(0.001) + 70^2(0.008) + 30^2(0.064) +10^2(0.921)]
=200
SD=rt(200-43.56)
=12.507

Yes, correct, (-10)² = 10

:smile:

Nice work!

Reply 6

shrek

OP

1

Thats it. It was the minus which threw me. Thanks very much for all the help.

Reply 7

Jack

I think your probabilities maybe wrong:
P(lemons) = 0.4, P(oranges) = 0.1, P(cherries) = 0.2, P(plums) = 0.3
So:
3 oranges = (0.1)^3
3 cherries = (0.2)^3
2 oranges/1 cherry = (0.1)^2*(0.2)*(3!/2!)
3 lemons = (0.4)^3
Lose = 1 - above answers added = 0.921

Reply 8

Jack

Do you agree?

S1 Little Problem

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