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? (Round your answer to three decimal places.)

Question

kropot72 · Answer

You need to find the separate probabilities that 8, 9 and 10 of the words on the test are words that the student knows. Next these 3 values of probability are added to find the probability that at least 8 of the words on the test are words that the student knows.
Do you want me to help you through the work?

anonymous · Answer

please?

kropot72 · Answer

$$P(8\ words\ known)=\frac{{16 \choose 8}{4 \choose 2}}{{20 \choose 10}}$$
Can you calculate the above step?

anonymous · Answer

yes, thank you

kropot72 · Answer

Can you please post your result. Then we can move on to the next step.

anonymous · Answer

That answer equals 2, and i thought probability had to be between 0 and 1

kropot72 · Answer

I get a result for P(8 words known) that is less than 1. Can we go thru your calculation?

anonymous · Answer

what I got is 2*2/2 or 4/2 = 2

kropot72 · Answer

Are you familiar with combinations and permutations. In the calculation for P(8 words known) 
$${16 \choose 8}$$
means 16 choose 8. Do you know how to calculate this combination?