Question

A student studying for a vocabulary test knows the meanings of 14 words from a list of 22 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.)

Answer 1

List has 26 words
Student knows meaning of 14
Student doesn't know meaning of 12

Probability student knows exactly 8 words on the test
= P(student knows exactly 8 words, and doesn't know 2 words)
= C(10,8) * (14/26 * 13/25 * 12/24 * 11/23 * 10/22 * 9/21* 8/20 * 7/19) * (12/18 * 11/17)
= 1386/37145

Probability student knows exactly 9 words on the test
= P(student knows exactly 9 words, and doesn't know 1 word)
= C(10,9) * (14/26 * 13/25 * 12/24 * 11/23 * 10/22 * 9/21* 8/20 * 7/19 * 6/18) * (12/17)
= 168/37145

Probability student knows exactly 10 words on the test
= C(10,10) * (14/26 * 13/25 * 12/24 * 11/23 * 10/22 * 9/21* 8/20 * 7/19 * 6/18 * 5/17)
= 7/37145

Probability student knows at least 8 words on the test
= 1386/37145 + 168/37145 + 7/37145 = 1561/37145 = 0.042