# helpp plz

• May 6th 2006, 02:04 PM
skhan
helpp plz
I was wondering if someone could help me solve this probability problem below.

Each week Bob and three friends fromw ork pool their money together and buy 12 lottery tickets that are randomly and equally divided up among the group.

a) In lotto mania, the game played by Bob and his friends, 6 winning numbers are seletced by random sampling w/o replacement from a bin of balls numbered 1 through 30. A player wins if the 6 numbers on his/her ticket match at least 5 numbers from the six winning numbers (order is irrelevant). If you buy a single ticket, what is the probability that you will win something? ANS: 0.0002442
• May 6th 2006, 10:23 PM
CaptainBlack
Quote:

Originally Posted by skhan
I was wondering if someone could help me solve this probability problem below.

Each week Bob and three friends fromw ork pool their money together and buy 12 lottery tickets that are randomly and equally divided up among the group.

a) In lotto mania, the game played by Bob and his friends, 6 winning numbers are seletced by random sampling w/o replacement from a bin of balls numbered 1 through 30. A player wins if the 6 numbers on his/her ticket match at least 5 numbers from the six winning numbers (order is irrelevant). If you buy a single ticket, what is the probability that you will win something? ANS: 0.0002442

There are $\displaystyle 30 \choose 6$ possible outcomes of the draw.

Of these exactly $\displaystyle 1$ matches all six of your numbers.

Also there are exactly 24 which match all but you smallest number (that
is the miss-matched number can be any of the numbers other than the
five matched or the unmatched number)

The same goes for the cases where it is the next smallest that is mis-matched, and the next ..

So there are $\displaystyle 1+24+24+24+24+24+24=1+6\times 25$ winning outcomes.
Therefore the probability $\displaystyle P$ of winning is the ratio of the number of
winning outcomes to the number of all outcomes, so:

$\displaystyle P=\frac{1+6 \times 24}{{30 \choose 6}}=\frac{145}{593775}\approx0.0002442$

RonL
• May 7th 2006, 12:48 PM
skhan
Thanks Ron! This helps me to do the rest of the questions on my own :)