Question

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

Answer 1

P(knows a word from the list) = 16/20 = 4/5 =0.8.
Using the binomial distribution:
\[\large P(knows\ 8\ out\ of\ 10)=10C8\times(0.8)^{8}\times(0.2)^{2}\]
\[\large P(knows\ 9\ out\ of\ 10)=10C9\times(0.8)^{9}\times0.2\]
\[\large P(knows\ 10\ out\ of\ 10)=(0.8)^{10}\]
When you have calculated the above 3 values of probability, add them to find the probability that at least 8 of the words on the test are words that the student knows.