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 f
rom 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.)
The sample space is 22 words and out of it, 14 words are known to have meanings for the student. In the problem, we use 10 C8 + 10 C9 + 10 C10 to associate at least 8 words. The complete formula is (10 C8 * (14/22)^8 * (8/22)^2 + 10 C9 (14/22)^9 * (8/22)^1 + 10 C 10 (14/22)^10 * (8/22)^)0) that is equal to 0.233
At least 8 of the words on the test are words that the student knows means that student knows 8 or 9 or 10 words.
1. Student knows 8 words (2 words are unknown): he knows the meanings of 14 words from a list of 22 words (8 words are unknown), then the number of ways to select 8 known words from 14 and 2 unknown words from 8 is
.
2. Student knows 9 words (1 unknown): he knows the meanings of 14 words from a list of 22 words, then the number of ways to select 9 known words from 14 and 1 from 8 is
.
3. Student knows 10 words: he knows the meanings of 14 words from a list of 22 words, then the number of ways to select 10 known words from 14 is
.
4. He has ways to select arbitrary 10 words from 22.
5.. The probability that at least 8 of the words on the test are words that the student knows is
Isolate x by adding 8 to both sides. 3 = x/3 Then, multiply by 3 on both sides. 9 = x To prove that this is right, you can imput 9 into the equation and it equals -5.