# Math Help - Probability for prizes!

1. ## Probability for prizes!

Hi all,
Could someone help me with a problem please?

I have 32 rounds and in each round there are 6 possible outcomes. Could someone please give the basic working of the probability of getting i.e. 5 out of 32 correct, or 10 out of 32 correct. Or even 5-9 out of 32, or 10-14 out of 32.
Thanks

Lee

2. ## Re: Probability for prizes!

if only one of the 6 is correct, and you choose randomly, and the outcome of each round is independant of the other rounds, then...

...You are describing a case of the binomial distribution.

With the following:
probability of success (p) = 1/6
probability of failure (q) = 5/6
number of trials (n) = 32

the chance of getting exactly X guesses right is given by the formula $^nC_r \times p^x \times q^{n-x}$

if you want to work out the chance of getting a range of values (5-10) then add up the chance of getting 5,6,7,8,9,10.

There are online tools that calculate these for you: Binomial Calculator