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Probability question has me stumped

If anyone could help me out with this question I would be so grateful. I thought I knew how to do it but my answer is very different from the one in the book.

At a fairground you can play spin and win. The game involves spinning a spinner with 5 equal sections numbered 1 to 5.
Spin the spinner three times
Three 5s win £15
Two 5s win £10

Throughout the day 250 play the game at £2 a go.

Estimate how much profit the stallholder will make if he charges £2 a go
Estimate the minimum that the stallholder should charge if he is not to make a loss

The answer is £230 and £1.08.

Thanks
Reply 1
Avatar for Zacken
Zacken
22
Original post by JayD29
If anyone could help me out with this question I would be so grateful. I thought I knew how to do it but my answer is very different from the one in the book.

At a fairground you can play spin and win. The game involves spinning a spinner with 5 equal sections numbered 1 to 5.
Spin the spinner three times
Three 5s win £15
Two 5s win £10

Throughout the day 250 play the game at £2 a go.

Estimate how much profit the stallholder will make if he charges £2 a go
Estimate the minimum that the stallholder should charge if he is not to make a loss

The answer is £230 and £1.08.

Thanks


What is the probability of getting a 5? It's 1/5.

So the probability of getting 3 5's in 3 turns is 1/5 * 1/5 * 1/5.

The probability of getting 2 5's in 3 turns is P(5)P(5)P(not 5) + P(5)P(not 5)P(5) + P(not 5)P(5)P(5) = 3 * 1/5 * 1/5 * 4/5 (not sure if you've heard of the binomial distribution before...)

So the probability of getting (not 2 5's and not 3 5's) is 1 - (sum of your previous answers)

So the expected profit is 2 * P(not 2 5's and not 3 5's) + 8 * P(2 5's) + 13 * P(3 5's).
Reply 2
Avatar for JayD29
JayD29
OP
Thanks so much, that makes sense.
I'd forgotten to include the P(not 5) when spinning 2 fives.
Got the right answer now :smile:
Reply 3
Avatar for Zacken
Zacken
22
Original post by JayD29
Thanks so much, that makes sense.
I'd forgotten to include the P(not 5) when spinning 2 fives.
Got the right answer now :smile:


Awesome!

Well done. :woo:

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