There are 40 marbles in an​ urn: (PROBABILITY)

Question

There are 40 marbles in an urn: 11 are green and 29 are yellow. You reach into the urn and randomly select 4 marbles without replacement. What is the probability that at least one of the marbles is​ green?

Answer 1

Find the probability that all 4 are not green, then subtract that from 1 to get the probability that at least one is green.

P(no green) = 29/40 x 28/39 x 27/38 x 26/37

P(no green on 1st draw) = 29/40

P(no green on 2nd draw) = 28/39

P(no green on 3rd) = 27/38

P(no green on 4th) =26/37

Just multiply those 4 probabilities together, then subtract the product from 1 to get

the probability of at least one green in 4 draws, without replacement

first draw there's 29 ways to get yellow out of 40 total ways

2nd draw there's 28 ways to get yellow out of 39 total ways

etc.