The prior probabilities for events A1 and A2 are P(A1) = 0.35 and P(A2) = 0.55. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits.   (a) Are A1 and A2 mutually exclusive?   - Select your answer -YesNoItem 1   Explain your answer.   The input in the box below will not be graded, but may be reviewed and considered by your instructor.           (b) Compute P(A1 ∩ B) and P(A2 ∩ B).   P(A1 ∩ B) =   P(A2 ∩ B) =       (c) Compute P(B).   P(B) =     (d) Apply Bayes’ theorem to compute P(A1 | B) and P(A2 | B).   P(A1 | B) =   P(A2 | B) =

T1.8 Let A and B be two events with probabilities P(A)=.35, P(B)=.40 and  P(A  U B)=.6. a) Find P(A intersection B)  b) Find P(A | B) c) Are events A and B independent or not?

K Find P(A or B or C) for the given probabilities. P(A)=0.39, P(B) = 0.22, P(C) = 0.11 P(A and B) = 0.12, P(A and C) = 0.02, P(B and C) = 0.07 P(A and B and C) = 0.01 P(A or B or C) =

9. By rewriting the formula for the Multiplication Rule, you can write a formula for finding P(A and B) conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B| A) = P(A) the information below to find the probability that a flight arrives on time given that it departed on time. The probability that an airplane flight departs on time is 0.92. The probability that a flight arrives on time is 0.86. The probability that a flight departs and arrives on time is 0.83. The probability that a flight arrives on time given that it departed on time is (Round to the nearest thousandth as needed.) . Use

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls)| P(x) |x(girls)| P(x) 0.000 0.122 10 0.061 1 0.001 0.183 11 0.022 2 0.006 7 0.210 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 Find the probability of selecting 12 or more girls. 0.001 O 0.022 0.006 O 0.007

q15A -

Suppose that events A and B are mutually exclusive with P(A) =  1 2 and P(B) =  1 6 . (Enter your answers as fractions.) (a) Are A and B independent events? Explain how you know. Since the events are mutually exclusive we know P(A|B) = which     P(A) and thus the events are     . (b) Are A and B complementary events? Explain how you know. We know that P(A) + P(B) = . And, since P(A) + P(B)     1, the events A and B     complementary events.