A student studying for a vocabulary test knows the meanings of 16 words from a list of 20 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows?

Question

anonymous · Answer

at least 8 means 8 or 9 or 10 so you have to compute these separately and add

anonymous · Answer

But how do I do that?

anonymous · Answer

number of ways to pick 10 out of 20 is $\binom{20}{10}=184756$so that is your denominator

anonymous · Answer

so the numerator would be (8 over 10)?? But what about the 16?

anonymous · Answer

lets do 10 first, because that is the easiest.  number of ways to choose 10 out of the 16 that he knows is $\binom{16}{10}=8008$ so that is your numerator for the probability that he knows all ten

anonymous · Answer

i.e. the probability that he knows all ten is 
$$\frac{\dbinom{16}{10}}{\dbinom{20}{10}}=\frac{8008}{184765}$$

anonymous · Answer

now for nine out of the ten. that means he has gotten 9 form the 16 he knows and 1 from the other 4 he does not, so that answer would be 
$$\frac{\dbinom{16}{9}\times \dbinom{4}{1}}{\dbinom{20}{10}}$$

anonymous · Answer

and finally for 8 out of ten, he got 8 from the 16, 2 from the other 4, so that would be 
$$\frac{\dbinom{16}{8}\times \dbinom{4}{2}}{\dbinom{20}{10}}$$ i will leave it to you to compute these numbers and add

anonymous · Answer

ok thank you!

anonymous · Answer

yw