A student studying for a vocabulary test knows the meanings of 16 words from a list of 26 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 probabilities that the student knows 8, 9 and 10 words, then add these three probability values.
$$P(8\ words)=\frac{C(16, 8) \times C(10, 2)}{C(26, 10)}=you\ can\ calculate$$
When you have calculated P(8 words) I can help you find P(9 words) and P(10 words).

anonymous · Answer

8 words =0.109?

kropot72 · Answer

Good work! You are correct. This question is being solved using the hypergeometric distribution. Have you studied this distribution?

anonymous · Answer

nope

kropot72 · Answer

$$P(9\ words)=\frac{C(16, 9) \times C(10, 1)}{C(26, 10)}=you\ can\ calculate$$

anonymous · Answer

9 =0.0027

anonymous · Answer

10=0.0015

kropot72 · Answer

Your answer for P(9) is not the same as mine. Please check.

anonymous · Answer

0.0215

kropot72 · Answer

Correct! Your result for P(10) is correct. Now add the three probability values.

kropot72 · Answer

The probability values are added, the reason being that the three events are mutually exclusive.

anonymous · Answer

thanks that makes so much sense to me now

kropot72 · Answer

You're welcome :)