Probability of A given B? AP Statistics

Test Preparation AP Test Preparation
1

<p>Barrons AP Statistics: Example 9.10</p>

<p>P(A|B)=?</p>

<p>If 90% of the households in a certain region have answering machines and 50% have both answering machines and call waiting, what is the probability that a household chosen at random [and found to have an answering machine also] has call waiting?</p>

<p>should the part in brackets be there? We want to find the probability of call waiting, not call waiting and answering machines right?</p>

<p>They give P(A intersection B)=.5 for answering machines and call waiting</p>

<p>They give P(B)=.9 for answering machines</p>

<p>We want to know P(A|B) for call waiting.</p>

<p>Should the part in brackets in the question be there?</p>

<p>We already know the probability of a household chosen at random with an answering machine and call waiting right?</p>

2

<p>Yes, the part in brackets seems to be intended. Otherwise the probability can’t be determined.</p>

<p>You want to find the probability that a household has call waiting, given that it has an answering machine. P(A|B) = P(A∩B)/P(B) = .5/.9 = 5/9.</p>

3

<p>another question, [Venn</a> Diagrams (optional)](<a href=“OpenStax”>OpenStax)</p>

<p>in example 3, are the events not mutually exclusive and not independent?</p>

<p>to be independent, C*PT should equal .05 but it equals .2 using the other values given</p>

4

<p>Yup, you’re right. The events are neither mutually exclusive nor independent. </p>

<p>P(C)*P(PT)≠P(C and PT)
(.4)(.5)≠(.05)
(.2)≠(.05), so the events are not independent.</p>

5

<p>thanks for the help guys!</p>