Key to practice exam 2.


1) The answer is E.

2) The correct answer is D. (That is D is false.)

3) The correct answer is D. The first two statements are wrong as they refer to individual people, not a mean. Statement C is wrong as it implies that the true mean is a random variable, which it is not. So none of A to C are correct.

4) Note P(A | B)=P(A and B)/P(B)=0.4/0.5=0.8 so (i) is false. P(A and B) is not P(A)xP(B), so A, B are not independent, so (ii) is true, (iii) is false as P(A and B) is not 0, so B.

5) The correct answer is C. Can have BBB. So P(A)=1/8.

6) The correct answer is B. It's clearly 1/2, and also the options are BGB, BBB, GBG, GGG. So P(B)=4/8=1/2.

7) The correct answer is A. The options are GGG, GGB, GBG, GBB so P(C)=4/8=1/2.

8) The event "A and B" means that they  have only boys and the first child is the same gender as the second. The only possibility is BBB, so P(A and B)=1/8. A.

9) E. "A and C" means they have all boys and the first is a girl. This is impossible. So P(A and C)=0.

10) For independence of A and B, we would need P(A and B) = P(A) P(B). That is we need 1/8 = 1/8x 1/2. Since this equation is not satisfied, we can say A and B are dependent. Similarly for A and C, we need P(A and C) = P(A) P(C), ie 0 = 1/8 x 1/2. Since this is  not satisfied, we say A and C are dependent. So the correct answer is D.


The table should look like this....


employee has taken drug

employee has not taken drug


positive result on test

90(=90% of 100)

45 (=5% of 900)


negative result on test





100 (=10% of 1000)



Out of 865 with a negative result, 10 had taken the drug, so this is a percentage of 10/865= 1.2%. The correct answer is then C.


12) The answer is C is the only one that cannot happen. Recall that P(A|B)=P(A and B)/P(B). P(A|B)=0 would imply P(A and B)=0, that is A, B disjoint, which means we can use rule 4 to say P(A or B)=P(A)+P(B)=0.3+0.8=1.1. But this is a number larger than 1, which violates rule 1. (Tricky, you have to use rule 6, rule 4 and rule 1!)

13) 68-95-99.7 rule tells you that its 0.16, that is E.

14) Now use the CLT to state that the sample mean has an N(298, 1) distribution, so now we are 3 sds from the mean, so (1-0.997)/2=0.0015 or 0.15%, so C.

15) B

16) =0x0.3+1x0.3+2x0.2+3x0.2=1.3, so D.




    (a) T. 15.5 is halfway inbetween the points.
    (b) T
    (c) T. A 99% interval totally contains a 95% interval calculated from the same data.
    (d) F. For disjoint events, P(A and B) = 0.
    (e) F. For independent events, P(A and B) =P(A)P(B).