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The prior probabilities for events   are  . It is also known that  Suppose P(B | A1) = .20 and  

The prior probabilities for events    It is also known that    Suppose  .

Are events   mutually exclusive?

Compute  

Compute   

Compute P(B) (to 4 decimals).

Apply Bayes' theorem to compute   decimals).

Also apply Bayes' theorem to compute   (to 4 decimals).

 

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Sumant
SumantLv10
6 Mar 2021

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Can two events with nonzero probabilities be both independent and mutually exclusive? Choose the correct answer below.

A. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities add up to one.

B. No two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability o the other must be zero.

C. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal.

D. No, two events with nonzero probabilities cannot be independent and mutually exclusive because independence is the complement of being mutually exclusive.

Suppose that A, B, and C are mutually independent events and that P(A) = 0.5, P(B) = 0.8, and P(C) = 0.9. Find the probabilities that (a) all three events occur, (b) exactly two of the three events occur, and (c) none of the events occurs.

9. Identify why this assignment of probabilities can not be legitimate.

 

a. P(A & B) can not be greater than either P(A) or P(B).

b. A and B are not given as mutually exclusive events.

c. P(A|B) is not known.

d. A and B are not given as independent events.

e. none of these.

 

10. Suppose a box contains 3 detective light bulbs and 12 good bulbs. Two bulbs are chosen from the box without replacement. Find the probability that one of the bulbs drawn is good and one is defective.

A. 12/35

B. 6/35

C. 3/14

D. 3/70

E. None of these

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