STATS 7 Lecture 4: Stats Homework #4
Edgar Mancia
Dr, Baldi, Stats 7
Stats 7 Homework #4
Chapter 7
18. Playing the same lottery number 1,000 times (odds being 1/1000) does not
guarantee you will win. Each drawing is an independent event therefore the
outcome of any previous games has no influence over the probability that you will
win on this particular game.
24. A) They are independent because the outcome of the first coin tossed does not
affect the outcome of the second coin. B) Not complimentary because they contain
the same simple events. C) Not mutually exclusive because they contain the same
simple event.
26. A and B are not independent because mutual exclusivity does not imply
independence. A and B are not complementary events because P(A) + P(B) does not
equal 1.
34. A = a woman is between 20 and 24
A’ = A woman is between 40 and 44
B = A woman is fertile
B’= A woman is not fertile
Conditional probabilities:
P (B|A) = 0.9
P B’|A= .
P B|A’= .
P B’|A’= .
35. If a random woman is selected her age and fertility status are not independent
because the probability of being fertile changes with age.
. a PA = . PA’ = . PB|A = . PB|A’ = .
b) The probability that the random voter belonged to Party A and voted for
candidate x. P (A and B) = P(B|A)P(A) = 0.44
c) The probability that the random voter did not belong to party A and voted for
candidate x. PA’ and B = PA’PB|A’ = .
d PB and A + PB and A’ = . = PB
e) Candidate X got 48.5% of the votes.
58. a) Yes because there is no reliable link between the three traits that would use
one of the traits to predict the other traits.
b) (1/50) (.2)(.3) = 0.0012
c) 10,000 (0.0012) = 12
d) 11/12
e) There is an 11/12 probability that the arrested person is innocent based on traits
and no other evidence so this is not a reasonable argument.
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