Question

If a bowl contains ten hazelnuts and eight almonds, what is the probability that four nut randomly selected from the bowl will all be hazelnuts?

Answer 1

`0.06862745 ~~6.9%`

Explanation:

We can model the bowl of nuts with a hypergeometric distribution containing 10 "successes" (hazelnuts) and 8 "failures" (almonds).

The formula we want to use is

`P(x=m)=(C_m^M*C_(n-m)^(N-M))/(C_n^N)`

Where:

`N=18` (the population size)
`M=10` (the number of successes in the population)

`n=4` (the sample size)
`m=4` (the number of successes we want in the sample)

Then the probability of getting 4 hazelnuts in a random sample of 4 nuts is:

`P(x=4)=(C_4^10*C_0^8)/(C_4^18)=(210*1)/(3060)~~0.06862745~~6.9%`