Sheldon Ross Introductory Statistics - Probability Section 4.4

1. P(did not sleep) = (216-128)/216 = 0.407

2.
(a) Gained weight = 5/32 = 0.15625
(b) Lost weight = 18/32 = 0.5625
(c) Neither lost nor gained weight = 9/32 = 0.28125

3.
(a) An ace = 4/52 = 0.076923077
(b) Not an ace = 0.923076923
(c) A spade = 13/52 = 0.25
(d) The ace of spades = 1/52 = 0.019230769

4.
(a) Exceeds 10,000 = 3/10 = 0.33
(b) Is under 3500 = 5/10 = 0.2
(c) Is between 4000 and 6000 = 0
(d) Is less than 2000 = 0

5.
TBD

6.
4/5

7.
(a) P (not in the program) = 56/100 = 0.56
(b) Addition rule - P(A ∩ B) = (26 + 28 - 44)/100 = 0.1

8. P(either dog or cat) = 20+32 -12 = 40
So P (neither) = 60/100 = 0.6

9.
(a) Either ring or necklace=40%, 0.4
(b) P(ring and necklace) = 20+30 - 40 = 10, 0.1

10.
(a) Does not play tennis = 120 - 44 = 76
(b) Does not play squash = 120 - 30 = 90
(c) Plays neither tennis nor squash - 0.64

11. Addition rule = 44 + 30 - 18 = 56

12.
(a) Either 7 or 11 = {(1,6), (6,1), (2,5), (5,2), (3,4), (4,3), (5,6), (6,5)}
P(Either 7 or 11) = 8/36 = 0.22

(b) One of the values 2, 3, or 12 = {(1,1), (1,2), (2,1), (6,6)}
P(One of the values 2, 3, or 12) = 4/36 = 0.11

(c) An even number = {(1,1), (1,3), (1,5), (3,1), (5,1), (2,2), (2,4), (2,6), (3,3), (3,5), ( 4,2), (6,2), (5,3)}
P(an even number) = 0.36

13. 1/19

14.
(a) Earns under $15,000 = 3936 / 81018 = 0.048581797
(b) Is a woman who earns between $20,000 and $40,000 = P(woman). P(range) = 0.386827619 x 0.300093806 = 0.116084573
(c) Earns under $50,000 = (22138(w) + 21364(m))/81018 = 0.54

15.
(a) The first key opens the door = 0.1
(b) All 10 keys are tried = 1/10
Here, prob that 1st key is not = 9/10
Once this is out of the way, prob that 2nd key is not = 8/9 (total 9 left)
And so on....
So P = 9/10 x 8/9 x 7/8 x .... 1/2 = 1/10 = 0.1

16.
(a) P(2nd) = 4/9 (position does not matter)
(b) P(charles is second) = P(second is boy). P(boy is charles) = 4/9 x 1/4 = 1/9

17.
(a) January 5 - 10/31
(b) August 12 - 9/31
(c) April 15 - 10/30
(d) May 15 - 11/31
(e) October 12 - 7/31