A Carnival game offers $100 cash prize for anyone who can break a balloon by throwing a dart at it.

It costs $5 to play, and you're willing to spend up to $20 trying to win.

You estimate that you have about a 10% chance of hitting the balloon on any throw.

What is the expected number of darts you'll throw?

What is the expected winnings ?

You have to draw up the PDF (probability distribution function) of this.

\begin{array}{|c|c|c|c|c|c|} \hline
X & 1&2&3&4&5 \\ \hline
P(X = x)&a &b&c&d&e \\ \hline \end{array}

Can you fill in the table?

The expected number of throws is given by:

\Sigma Xp(x) = (1\times a) + (2\times b) + ... + (5\times e)

Now, from this you can find the probability that you win $100 and from there, the total cost and finally, the profit/winnings.

Post what you get! :)

Hi, it it's a pdf and I'm limited to 4 games, 10% success rate, is it:

(1x 0.10) + (2 x 0.10) + (3 x 0.10) + (4 x 0.10) ?

for the # of throws ?

I researched it somewhat and found a formula for geometric progression.

If I may trouble you to explain the formula and process further, I'd be most grateful

I also don't know how to calculate the winnings amount either, sorry.

Thank you very much.

Sure.

What is the probability that you win on first shot? 0.1

What is the probability that you win on second shot? It means you lost on the first shot and won on the second, that is 0.9x0.1 = 0.09

What is the probability that you win on the third shot?
0.9x0.9x0.1 = 0.081

4th shot?
0.9^3 x 0.1 = 0.0729

Can you complete it now?

Then you find the expected throws using those new values.