Stat. 6304 (Fall, 2012) HW 2 Solutions
4.6 a. 1 in 4 (or 0.25) b. 1 in 106000.
4.14 600/12000 = 1/20=0.05.
4.17
a. P(A)=4/23.
b. P(B) = 0.
c. Yes, the events are mutually exclusive. A manager cannot collect less than 80% and between 85 and
89% simultaneously.
d. P(meets standard) = (2 + 13)/23 = 15/23.
4.41
a. P(woman) = 0.4; P(man) = 1 −P(woman) = 1 −0.4=0.6.
b. P(2consecutive women) = P(woman1)P(woman2) = (0.4)(0.4) = 0.16. Note that the first = is due to
independence.
4.42 P(A)=0.55 and P(B|A)>1/3.
4.44
a. 30/139
b. 21/139
c. P(not Anglo −Australian) = 1 −P(Anglo −Australian) = 1 −63/139 = 76/139.
d. P(close contact ∪Asian) = P(close contact)+ PAsian)−P(close contact ∩Asian) = 21+46−1
139 = 66/139.
e.
P(little or no contact|Asian) = P(little or no contact ∩Asian)
P(Asian) =37/139
46/139 = 37/46 '0.8043.
f.
P(little or no contact|Anglo −Australian) = P(little or no contact ∩Anglo −Australian)
P(Anglo −Australian)
=30/139
63/139 = 30/63 '0.4762.
g. Asians are most likely to have little or no contact with mentally ill people. (Note that this means that
etnicity is not independent of “little or no contact with mentally ill”.
4.60
a. 21/22.
b. P(“professor” correct) = 1 −8/22 = 14/22.
c. P( misspell “Gandhi” ∪“Khaki”) = P(misspell “Gandhi”) + P(misspell “khaki”) −P(misspell both) =
19/22 + 5/22 −3/22 = 21/22.
4.74 Events A(pregnant) and B(test positive and not pregnant) are mutually exclusive. Also, events Band
C(test negative and pregnant) are mutually exclusive.