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A boy is preparing for test. The teacher gives $30$ questions to study from and will select $10$ out of the $30$. The student only know hows to solve $25$ of the $30$ questions.
A)What is the probability that the student will get perfect on the test? B)what is the probability that the student will get at least $8$ questions correct?
I solved for A which is $11\%$, but I don't I have no clue how to solve B. Please give me a hint!
Note that $P(x \geq 8) = P(x=8) + P(x=9) + P(x=10).$
Here's a hint. I'll calculate the probability that the student gets exactly seven correct.
First, choose $7$ questions from the $25$ he knows ($_{25}C_7$). Then, choose $3$ from the $5$ he doesn't know ($_5C_3$).
Then the probability of getting a test that he knows exactly seven of them is
$$P(7) = \frac{_{25}C_7 \cdot _5C_3}{_{30}C_{10}}.$$
Can you take it from here?
If he get's at least 8 correct, that means he can get at most 2 wrong. Assuming he would never guess right (answer unknown question correctly), it makes more sense to figure out the probability that he will get 3 questions, 4 questions, or 5 that he doesn't want.
For example, the 4 questions he doesn't want on the test(Will only get 6 right): Choose 4 questions from the 5 he doesn't know : 5C4 Choose another 6 from the 20 he knows: 20C6 Then divide by the total ways of choosing 10 questions: 30C10. so: 5*38760/30045015 is about .6% ( I really hope I'm right here and not misleading you)
Could you get the 3 questions and 5 questions case then?
