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?

1 Answer
Mar 28, 2018

#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%#