6. Establish what is meant by (a) a pair of mutually exclusive events and (b)a pair of statistically independent events.Prove, with reference to the axioms of probability and the rules ofboolean algebra, thatP(AUB) = P(A) + P(B) – P(AN B).The probability that a smoker who consumes over 40 cigarettes a daywill suffer from chronic respiratory illness is 0.4. The probability that hewill suffer from heart disease is 0.5. The probability that he will sufferfrom at least one of these ailments is 0.6(i) Find the probability that the smoker will suffer from both ailments,(ii) Find the probability that he will suffer from heart disease given thathe suffers from chronic respiratory illness.

Solution: 6. Let A be the event that a smoker will suffer from chronic respiratory illness and B be…

Answered: Establish what is meant by (a) a pair…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Similar questions

Events A and B are mutually exclusive. Suppose event A occurs with probability 0.48 and event B occurs with probability 0.42. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that A does not occur or B does not occur (or both). (b) Compute the probability that either B occurs without A occurring or A and B both occur.
5.Prove the following properties of probability: P(A) = 1-P(A). b. For any events A and B, P(AUB) = P(A) + P (B) – P(AB). -
Show that the probability that an event A or an event B or both will occur is given by the formula P(AUB) = P(A)+P(B)– P(AnB), and specialise this formula for the case (a) when A, B are mutually exclusive events and for the case (b) where A, B are statistically independent events. Find the probabilities P(A), P(B) when A, B are statistically independent events such that P(B) = 2P(A) and P(AU B) = 5/8.
b. Determine P(F or D)= P(F or D). (Type an integer or a decimal.) c. Find the probability that a randomly selected adult is male. P(male) = (Type an integer or a decimal.)
Use the appropriate formula to answer the question: • Independent Probability: P(A and B) = P(A) x P(B) • Conditional Probability: P(A n B) = P(A) x P(B|A) • Addition Rule: P(A or B) = P(A) + P(B) – P(A and B) True or False: Events A and B are independent? P(A) = 0.60 P(B) = 0.70 P(A and B) = 0.42 True False
A student goes to the library. Let event A be that the student checks out a book and event B be that the student uses a library computer. Suppose that we happen to know that P (A) = 0.40, that P (B) = 0.30, and that P (B|A) = 0.5. Compute the following (1) P(Ac)(2) P(A AND B) (3) P(A|B)
P(A) + P(B) = 1 for any events A and B that are mutually exclusive. True False
O Whats inside of blo. S Watch Cra zy Rich A Car inspection: Of all the registered automobiles in a city, 6% fail the emissions test. Nine automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places. Part 1 of 4 (a) Find the probability that exactly four of them fail the test. The probability that exactly four of them fail the test is Part 2 of 4 (b) Find the probability that fewer than four of them fail the test. The probability that fewer than four of them fail the test is Part 3 of 4 (c) Find the probability that more than three of them fail the test., The probability that more than three of them fail the test is
Event E and event F are independent. Fiven P(E) = 0.3, P = (F) 0.5, compute P(E and F) and P(E or F). a) P(E and F) = b ) P(E or F)
a and b
Events A and B are independent. Suppose event A occurs with probability 0.19 and event B occurs with probability 0.76. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that A occurs but B does not occur. 0 (b) Compute the probability that B occurs or A does not occur (or both). 0 X Ś
Events A and B are mutually exclusive. Suppose event A Occurs with probability 0.58 and event B occurs with probability 0.32. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that B occurs but A does not occur. (b) Compute the probability that neither the event A nor the event B occurs.

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