Answers:
a) 0.018.
b) 0.614.
c) 0.166.
d) 0.479
Explanations:
1) Table
----------------------Male ----------- Female ---------- Total
Underwear ----- 0.220 ---------- 0.024 ---------- 0.244
Nightgown ----- 0.002 ---------- 0.180 ------------ 0.182
Nothing --------- 0.160 ----------- 0.018 ------------ 0.178
Pajamas --------- 0.102 ---------- 0.073 ----------- 0.175
T-shirt ------------ 0.046 --------- 0.088 ------------ 0.134
Other --------------0.084 --------- 0.003 ------------ 0.087
2) Check that it is a table of relative frequencies:
total = 0.244 + 0.182 + 0.178 + 0.175 + 0.134 + 0.087 = 1 ⇒ indeed this is a table of relative frequencies.
That means that each data is a probabiilty.
3) Soluitions:
(a) What is the probability that a traveler is a female who sleeps in the nothing?
relative frequency of females that use nothing = 0.018
(b) What is the probability that a traveler is male?
Probability that a traveler is a male = relative frequency of males = 0.220 + 0.002 + 0.160 + 0.102 + 0.046 + 0.084 = 0.614
(c) Assuming the traveler is male, what is the probability that he sleeps in pajamas?
It is the relative frequency of the males that sleep in pajamas divided by the relative frequency of males = 0.102 / 0.614 = 0.166
(d) What is the probability that a traveler is male if the traveler sleeps in pajamas or a T-shirt?
It is the relative frequency of males that sleep in pajamas plus that of the males that sleep in T-shirt, divided the total relative frequency of travelers that sleep in pajamas or T-shirt
i) relative frequency of males that sleeps in pajamas plus that of the males that sleeps in T-shirt = 0.102 + 0.046 = 0.148
ii) relative frequency of travelers that sleep in pajamas or T-shirt = 0.102 + 0.046 + 0.073 + 0.088 = 0.309
iii) quotient = 0.148 / 0.309 = 0.479
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