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Confusing Probability Question

A fairground game requires players to roll a coin across a table, on which is painted a grid
of square cells. If the coin lands completely inside a square cell, the player wins a prize;
otherwise no prize is won. The value of the prize is written inside the cells: 70% of the cells
have a £1 prize, 25% have a £5 prize, and 5% have a £20 prize. Each cell is equally likely
to be the one in which the coin lands.

Let θ denote the probability that the coin lands completely inside a cell, and denote by X
the amount of money won on a single roll of the coin.

(i) Write down the probability function of X, as a function of θ.

Now I don't understand how to make sense of all this information. So, if the player lands the coin on a square the probability is: (0.7x0.25x0.05)θ? and for not landing 1 - P(lands)

Thanks for your time

(edited 8 years ago)

Reply 1

ghostwalker

Original post by mathsRus

Now I don't understand how to make sense of all this information. So, if the player lands the coin on a square the probability is: (0.7x0.25x0.05)θ? and for not landing 1 - P(lands)

Thanks for your time

They're basically looking for a table, with column headings the values that X can take, and entries below of the probability that X takes that particular value.

Or some similar format.

Reply 2

mathsRus

Original post by ghostwalker

They're basically looking for a table, with column headings the values that X can take, and entries below of the probability that X takes that particular value.

Or some similar format.

I did a table

For X: 0 £1 £5 £20
______________________________
px(X): No idea 0.7θ 0.25θ 0.05θ

I do not understand the question in the first place. Like how many cells are there if they are equally likely to occur. Could you simplify the question?

Don't have the mark scheme

Reply 3

ghostwalker

Original post by mathsRus

I did a table

For X: 0 £1 £5 £20
______________________________
px(X): No idea 0.7θ 0.25θ 0.05θ

Yep.

And the only time X=0, is if it doesn't land wholly within the square, which has probability

1-\theta

as you had previously.

I do not understand the question in the first place. Like how many cells are there if they are equally likely to occur. Could you simplify the question?

Don't have the mark scheme

The number of cells doesn't matter - it's the percentage breakdown of the types of cells that is important.

The coin either does (probability

\theta

), or does not land in a cell.

Given that it does land in a cell then each cell is as likely as any other. So, the percentage of a given type tells you the probability of that type being selected.

Reply 4

mathsRus

Original post by ghostwalker

Yep.

And the only time X=0, is if it doesn't land wholly within the square, which has probability

1-\theta

as you had previously.

The number of cells doesn't matter - it's the percentage breakdown of the types of cells that is important.

The coin either does (probability

\theta

), or does not land in a cell.

Given that it does land in a cell then each cell is as likely as any other. So, the percentage of a given type tells you the probability of that type being selected.