Question

please confirm if my table is complete AND answer A, B and C

will rate. thank you!

1. (12 pts) Assume that the proportions of households that use streaming entertainment services in a particular city are as follows: Netflix (N): 61%; Amazon Prime (A): 36% N and A: 26% N= Neth (Recommendation: Construct and fill in a probability table Amazon yes Amazone NO Ivetflix yes 0.35 A- Amaz Pir Total 61 0.26 Ivet flix no 0.10 0.29 Total 36 64 If you select a random household in this city: 39 100 a) What is the probability that they use only one of these services? Plonly one) = P(NAC) + P ( NA) b) What is the probability that they do not have any of these services? c) What is the probability that they have only Amazon Prime?

Answer 1

Yes, your table is complete and is correct.

a) The probability that they use one of these services is given by:

$\begin{align*} P\left( {{\rm{only}}\;{\rm{one}}} \right) &= P\left( {N \cap {A^c}} \right) + P\left( {{N^c} \cap A} \right)\\ &= 0.35 + 0.10\\ &= 0.45 \end{align*}$

The probability that they use one of these services is 0.45.

b) The probability that they do not have any of these services is given by:

$P\left( {{N^c} \cap {A^c}} \right) = 0.29$

The probability that they do not have any of these services is 0.29.

c) The probability that they have only A is given by:

$P\left( {{N^c} \cap A} \right) = 0.10$

The probability that they have only A is 0.10.