Back"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
35. P(A) = 0.25, P(A') = 0.75, P(B|A) = 0.3 , and P(B|A') = 0.5 "
A rare condition affects 1 out of every 100 people. The test for this condition has the following probabilities: If a person has the condition, the test is correct 95% of the time. If a person does not have the condition, the test gives a wrong result 10% of the time. If A is the event 'tested positive' and B is the event 'has condition,' find P(B'), P(AIB), and P(A|B').
According to data from a metro station, 28% of trains are delayed. When compared to weather data, it was found that 73% of train delays and 35% of on-time rides were on days with precipitation. Given there is precipitation, what is the probability the train will be delayed?
"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
34. P(A) = 3/8, P(A') = 5/8, P(B|A) = 2/3 , and P(B|A') = 3/5 "
"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
38. P(A) = 12%, P(A') = 88%, P(B|A) = 66% , and P(B|A') = 19% "
"39. Reliability of Testing A virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time when the person has the virus and 5% of the time when the person does not have the virus. (This 5% result is called a false positive.) Let A be the event ""the person is infected"" and B be the event ""the person tests positive.""
a. Using Bayes' Theorem, when a person tests positive, determine the probability that the person is infected."
"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
36. P(A) = 0.62, P(A') = 0.38, P(B|A) = 0.41 , and P(B|A') = 0.17 "
Speeding Tickets
Use the results of Problem 44 in Section 5.2 to answer the following.
b. Among those who were issued no tickets last year, what is the probability the individual texts while driving?
Putting It Together: Success Sequence
Is there a ""path"" to success? Brookings scholars Ron Haskins and Isabel Sawhill suggest the path to success is: education, followed by work, followed by marriage, followed by children. Sociologists Wendy Wang and W. Bradford Wilcox tracked a cohort of young millennial adults from their teenage years to early adulthood (ages 28 to 34) and recorded information about their education, marital status, child-rearing, and income.
c. The article states that 31% of millennials who completed high school were below the poverty rate; 16% of millennials who had a high school diploma and a full-time job were below the poverty rate; and 3% of millennials who had a high school diploma, a full-time job, and put marriage before having children were below the poverty rate. Express each of these probabilities as a conditional probability.