## sleung Group Title A student who is taking a 30 question multiple choice test knows 24 of the answers. If the student doesn't know the answer, he chooses uniformly from 1 of 5 choices. Given that he gets a randomly chosen question right, what is the probability he guessed on the question? 6 months ago 6 months ago

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1. elvisg1993 Group Title

30!/(24!) * 1/5

2. sleung Group Title

How'd you get that elvis?

3. dumbcow Group Title

conditional probability $P(A | B) = \frac{P(A and B)}{P(B)}$ probability he guesses and gets it right = 1/5 probability the question is right = (24+6/5)/30

4. sleung Group Title

My exam says that the answer is 1/21. How do u get that?

5. dumbcow Group Title

oh sorry my P(AB) is wrong, it should be 1.2/30 $\frac{\frac{1.2}{30}}{\frac{25.2}{30}} = \frac{1.2}{25.2} = \frac{1}{21}$

6. sleung Group Title

Thanks a lot.

7. dumbcow Group Title

yw

8. sleung Group Title

How'd you get 1.2 and 25.2? Still not quite clear on that.

9. dumbcow Group Title

1.2 is the avg number of questions guessed correctly ---> 6*(1/5) 25.2 is avg total num of correct questions ---> 24 + 6/5

10. sleung Group Title

Thanks so much

11. sleung Group Title

For 0<x<y<z<1, the joint density of (X,Y,Z) is given by f(x,y,z)=48xyz. Find P(Y>1/2). I got .78, but my exam says it's .84.

12. dumbcow Group Title

$48 \int\limits_.5^1 \int\limits_y^1 \int\limits_0^y (xyz) dx dz dy$ $= 48 \int\limits_.5^1 \int\limits_y^1 \frac{y^3 z}{2} dz dy$ $= 48 \int\limits_.5^1 (\frac{y^3}{4} - \frac{y^5}{4}) dy$ $= 12(\frac{y^4}{4} - \frac{y^6}{6}) |_.5^1$ $= 1 - \frac{10}{64} = \frac{27}{32}$ = 0.84375

13. dumbcow Group Title

how did you go from pre-calc probability to multi-variable calculus?? lol

14. sleung Group Title

Haha, don't know - guess i should've asked that in the calc section. I was asked to find a probability though.

15. sleung Group Title

Insurance losses L in a given year have a lognormal distribution with L=e^X, where X is a normal random variable with mean 3.9 and standard deviation 0.8. If a $100 deductible and a$50 benefit are imposed, what is the probability the insurance company will pay the benefit limit given that a loss exceeds the deductible?

16. sleung Group Title

A fair 6-sided die is rolled 1,000 times. Using a normal approximation with a continuity correction, what is the probability the number of 3's rolled is greater than 150 and less than 180? I'm supposed to get .78, but instead I'm getting .81.