I did not take statistics at any point in my academic career. I kinda wish I had sometimes. This is one of those times.
I had 8 scratch off tickets. The odds of breaking even or better were listed as 1 in 4.32. I “won” 6 of those 8 tickets. How do I calculate the odds of this occurring? All the examples I have seen use a coin toss, which has a 50% chance, and I cannot figure out how to convert that process to this example. Can anyone help? Thanks.
tl;dr I won 6 of out 8 tickets, each has 1 in 4.32 odds. How unlikely was that?
Type
28*(1/4.32)^6*(1 - 1/4.32)^2
at the Google prompt to see 0.00254427602, or 2.54%.
In this expression all but the “28” should be clear. C(8,6) = 28 is the number of ways of choosing 6 objects out of 8. (C(8,6) = (C8,2) = 8*7/2.)
I see there are several Binomial Probability calculators available online, such as the ones here and here.
In your example, the number of trials (n) would be 8.
The number of successes (x) would be 6.
And the probability of success on each trial (p) would be, if I’m interpreting what you say correctly, 1 / 4.32, or 0.231481481.