Answered: Let A and B be events such that P (A) =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Show that if Ą and Ą are two events, then P(A) + P(A₂) −1≤ P(ĄCĄ).
A commuter must pass through three traffic lights on her way to work. For each traffic light, the probability that it is green when she arrives is 0.6. The lights are independent. 3 (a) Compute the probability that all three lights are green. (b) The commuter goes to work five days per week. Let X be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. Determine the distribution of X. (c) Calculate P(X= 3).
Let A and B be events with P(A) = 0.5, P(B) = 0.4. Assume that A and B are independent. Find P(A and B).
The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.65, the probability that a car brought into the shop requires brake repair is 0.35, and the probability that a car requires both an oil change and brake repair is 0.24. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair. The probability that the car requires an oil change or brake repair is (Type an integer or a decimal.)
A city has two daily newspapers, A and B. A survey of 100 residents of the city shows that 35 people subscribe to A, 60 subscribe to B and 20 subscribe to both. Find the probability that a resident chosen is subscribing to A only?
A building contractor buys 70% of his cement from supplier A and 30% from supplier B. A total of 70% of the bags from A arrive undamaged, while 90% of the bags from B arrive undamaged. Find the probability that an undamaged bag is from supplier B. The probability is nothing. (Type an integer or decimal rounded to four decimal places as needed.)
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
A certain disease has a prevalence of in a population. The rate of false 4 positives is 10% and and the rate of false negatives is 5%. If you are exposed to the disease, then probability that you contract it is . You can only contract the disease by sharing food. Suppose that you meet 10 people, that each person tests negative for the disease, and that you share food with each of them exactly three times. What is the probability that you contract the disease?
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.
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (1) the youngest is a girl, (ii) at least one is a girl?
a and b
Assume that we have two events A and B, that are mutually exclusive. Assume further that P(A): = 0.35 and P(B) = 0.45. Find P(A n B). Select one: O a. 0.35 О Б.0.1575 Oc. 0.65 O d. 0.45 O e. 0 O f.0.55

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Let A and B be events such that P (A) = 4/10 and that P (A∪B) = 7/10 Find the probability of B assuming that A and B are independent.