SOLUTION: 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

P(knows at least 8 words) = P(knows exactly 8 words) + P(knows exactly 9 words) + P(knows all 10 words).



(a)  P(knows exactly 8 words) =  = .


     The denominator of the fraction shows in how many ways 10 different words can be selected for the test from the total of 20 words.
     It is the the number of elements in the total sample space.

     The numerator of the fraction shows in how many ways these selected 10 words can be comprised using 8 known words of 16 
     and 2 unknown words from remaining 4 unknown words.
     
     It is the number of favorable events (elements of the sample space).

     Then the ratio is the probability for this configuration.



(b)  P(knows exactly 9 words) =  = .


     The explanation is similar to (a).



(c)  P(knows all 10 words) = .


Calculate each expression (a), (b) and (c) separately; then add to get the final probability value.