Answer:
5/4324 = 0.001156337
Step-by-step explanation:
To better understand the hyper-geometric distribution consider the following example:
There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).
We extract a random sample of 30 senators and we want to answer this question:
What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?
The answer using the h-g distribution is:
Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).
<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be
Now compute each combination separately:
and now replace the values:
and that is it.
If the decimal expression is preferred then divide the fractions to get 0.001156337