Probability help !!!

2014-10-13 4:35 am
A financial analyst finds that 75% and 40% of his clients invest in the
stock market and the bond market respectively. It is also found that 25%
of his clients invest in both markets.
a Suppose that one of his clients is randomly selected,

1)What is the probability that the client has invested either in the
stock market or in the bond market or both?

2)What is the probability that the client has invested in the bond
market but not in the stock market?

3) What is the probability that the client has neither invested in the
bond market nor in the stock market?

4)If the client is known to have invested in the bond market, what is
the probability that he or she has not invested in the stock market?


2 A restaurant has collected data on its customers’ orders and has estimated empirical probabilities of what happens after a main course. It is found that 20% of customers have dessert only, 40% have coffee only, and 30% have both dessert and coffee.

a Find the probability that a customer orders coffee after a main course.
b Find the probability that a customer orders either coffee or dessert.
c Find the probability that a customer who orders dessert also orders coffee.
d Find the probability that a customer who does not order coffee does order dessert

回答 (1)

2014-10-13 6:24 am
✔ 最佳答案
1.
1)
S : client investing in the stock market
B : client investing in the bond market

P(S) = 75%
P(B) = 40%
P(S∩B) = 25%

P(SUB)
= P(S) + P(B) - P(S∩B)
= 75% + 40% - 25%
= 0.9

2)
P(S'UB)
= P(B) - P(B∩S)
= 40% - 25%
= 0.15

3)
P(S'∩B')
= 1 - P(SUB)
= 1 - 90%
= 0.1

4)
P(S'|B)
P(S'∩B) / P(B)
= 15% / 40%
= 0.375


====
2.
a.
D : customer having dessert only
C : customer having coffee only

P(D∩C') = 20%
P(D'∩C) = 40%
P(D∩C) = 30%

P(C)
= P(D'∩C) + P(D∩C)
= 40% + 30%
= 0.7

b.
P(D or C)
= P(D∩C') + P(D'∩C)
= 20% + 40%
= 0.6

c.
P(C|D)
= P(D∩C) / P(D)
= P(D∩C) / [P(D∩C) + P(D∩C')
= 30% / (30% + 20%)
= 0.6

d.
P(D|C')
= P(D∩C') / [1 - P(C)]
= 20% / [1 - 70%]
= 2/3


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