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).-

Solution-:We want to prove the following properties of probability:(a) (b)

Answered: 5.Prove the following properties of…

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...

See similar textbooks

Similar questions

Leo is a very average golfer. The probability that he hits a bad shot at any time is 0.4, independent of the outcome of any other shot. In a round of golf, the probability that Leo's first bad shot is his fifth shot is Select one: O (0.4) (0.6)' O (0.4)5 O (0.6)* (0.4)' O (0.6) (0.4)'
Events A and B are independent. Find the indicated ProbabilityP(A) = 0.02P(B) = 0.27P(A and B) =
The table below shows the results of a survey that asked 1062 adults from a certain country if they favored or opposed a tax to fund education A person is selected at random. Complete parts (a) through (c) Males Females Total Support 170 238 408 Oppose 326 296 622 Unsure 8 24 32 Total 504 558 1062
Q 10 A building contractor buys 70% of his cement from supplier A and 30% from supplier B. A total of 80% of bags from A arrive undamaged, while 85% of the bags from B arrive undamaged. Give the probability that a damaged bag is from the supplier A. (P(A|D))
According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows. P(A) • P(B| A) P(A) • P(B| A) + P (A') •P(B| A') P(A| B) = %3D Use Bayes' Theorem to find P(A B) using the probabilities shown below. P(A) =1. P(A') =, P(B| A) =5, 1 and P(B| A') = %3D %3D 10 %3D 4 The probability of event A, given that event B has occurred, is P(A B) =|. (Round to the nearest thousandth as needed.)
If P (A) = 0.6, P (B) =0.5 and P (A U B) = 0.9, find the following probabilities: (a) P (ANB) (b) P (A/B)
You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent
According to Bayes' Theorem, the probability of event A, given that event B has occurred, is as follows. P(A) P(BA) P(A) P(BA) + P(A) P(BA) Use Bayes' Theorem to find P(A| B) using the probabilities shown below. P(A| B)= 1 1 P(A) = 6' ) = -5₁₁ P (A) = ₁ P(B| A) = 77₁ and P (B| A') == 6' 2 The probability of event A, given that event B has occurred, is P(A| B) = (Round to the nearest thousandth as needed.)
Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

5.Prove the following properties of probability: P(A) = 1-P(A). b. For any events A and B, P(A U B) = P(A) + P(B) – P(AB).