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.

Answer 1

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