# lottery question real odds

• Apr 8th 2010, 09:07 AM
jickjoker
lottery question real odds

a lottery has 45 balls (1 to 45)
6 balls are randomly generated each week

you can choose the amount of numbers you want to play
example
you can pick 1 number and it pays 6 to 1 if your 1 number comes up in one of the 6
numbers

1. question
I decide to bet £1 on 3 numbers 16 17 23 , which pays 600 to 1 ,
what are the real odds of hitting all 3 of my numbers and bagging
600 smackeroons!

2. what is the ev for this game?

tx
• Apr 8th 2010, 02:18 PM
awkward
Quote:

Originally Posted by jickjoker

a lottery has 45 balls (1 to 45)
6 balls are randomly generated each week

you can choose the amount of numbers you want to play
example
you can pick 1 number and it pays 6 to 1 if your 1 number comes up in one of the 6
numbers

1. question
I decide to bet £1 on 3 numbers 16 17 23 , which pays 600 to 1 ,
what are the real odds of hitting all 3 of my numbers and bagging
600 smackeroons!

2. what is the ev for this game?

tx

The probability of hitting all 3 numbers is
$\displaystyle \frac{\binom{42}{3}}{\binom{45}{6}} \approx 0.001409$

The expected value is approximately
$\displaystyle 0.001409 \times 600 - 1 = -0.15$
• Apr 8th 2010, 07:29 PM
macosxnerd101
Since we have 45 unique balls, each time we pick one, the chances of drawing the others increases. So the probability of drawing all three is (3/45) * (2/44) * (1/41). As assuming we pick one of your 3 numbers on the 1st try, we have the other two remaining out of 44.