The probability that a household subscribes to HBO or Netflix is 0.80. Furthermo
ID: 3352077 • Letter: T
Question
The probability that a household subscribes to HBO or Netflix is 0.80. Furthermore, the probability that a household subscribes to HBO is 0.25, and the probability that household does not subscribe to Netflix is 0.31.
a) Define the events.
b) Write down the given probabilities { i.e. P(__) = __ }.
c) What is the probability that a household subscribes to Netflix? Use proper notation {i.e. P(_)=_}.
d) What is the probability that a household subscribes to HBO and Netflix?
e) What is the probability that a household that subscribes to Netflix subscribes to HBO?
f) Are the events subscribing to HBO and subscribing to Netflix independent? Explain mathematically.
Explanation / Answer
a) Event A: household subscribes to HBO
Event B: Household subscribes to Netflix
b) P(A ) =0.25
P(B) =1-P(B') =1-0.31 =0.69
P(AUB) =0.80
c) P(netflix) =P(B) =1-P(B') =1-0.31 =0.69
d) P(AnB) =P(A)+P(B)-P(AUB)
=0.25+0.69 -0.80
=0.94-0.80
=0.14
e) P(HBO given that it subscribes to netflix) =P(A | B) =P(AnB)/P(B)
= 0.14/0.69
=14/69
f) these events are independent if P(AnB) =P(A)*P(B)
0.14 =0.25*0.69
0.14 =0.1725
Clearly,P(AnB) is not equal to P(A)*P(B)
Hence,the events subscribing to HBO and subscribing to Netflix are not independent
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