S1 - Expectation!

From Heinemann S1 8B Q10:

"At a fair a roll-a-penny stall can be played with 1p or 2p coins. If the coin lands inside a square, the player receives the coin plus 2 other coins of the same value, otherwise the coin is lost. The probability of winning the coin with 1p is

\frac{19}{40}

and the probability for a 2p coin is

\frac{11}{40}

."

a) Find the expected winnings for each coin.

Presumably this means find E(something) although I have no idea about how to do this. I've tried to draw a probability distribution but I failed.

Can someone please help?

Reply 1

Chaoslord

16

from what i remember expection is the mean outcome? anyone back me up on this i haven't done stats for a while

consider it like this, in 40 throws how many times would you expect to lose your 1p?

21, thats -21p

in 40 throws how many times would you expect to win 2p? 19, thats + 38p

so expectation is (38-21)/40

in other words, do expected outcome x probabilty, sum these all up for the expectation and you get your answer =]

Reply 2

jonny23563

12

Expectation is just how much you can expect to win. So for example, in the National Lottery, you pay a pound for a ticket, half of that goes to the prize fund, so the expectation is 50p.

So here, you've got a chance of winning 3p

\frac {19}{40}

of the time and a chance of winning 0p

\frac {40 - 19}{40}

of the time. Does this help?

Reply 3

stumpy07

Expectation is the (prob of winning)*(what you win), summed for all possibilities.

Reply 4

electriic_ink

OP

15

Chaoslord

from what i remember expection is the mean outcome? anyone back me up on this i haven't done stats for a while

consider it like this, in 40 throws how many times would you expect to lose your 1p?

21, thats -21p

in 40 throws how many times would you expect to win 2p? 19, thats + 38p

so expectation is (38-21)/40

in other words, do expected outcome x probabilty, sum these all up for the expectation and you get your answer =]

Thank you. That's what I was looked for :smile:

S1 - Expectation!

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