A construction firm bids on two different contracts. Let E, be the event that the bid on the first contract is successful, and define E, analogously for the second contract. Suppose that P(E,) = 0.3 andP(E,) = 0.7 and that E, and E, are independent events.(a) Calculate the probability that both bids are successful (the probability of the event E, and E,).(b) Calculate the probability that neither bid is successful (the probability of the event (not E,) and (not E,)).(c) What is the probability that the firm is successful in at least one of the two bids?

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Answered: A construction firm bids on two…

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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2 Producers (A and B) supply car mirrors to a distributor. If a mirror is picked up at random, the probability that it is from A is 0.25, from B it is 0.75. Due to the manufacturer’s failure, some mirrors are defective. The probability that mirror by A is defective is 0.04. The probability that mirrors by B is defective is 0.02. Find out the probability that a mirror selected at random will be defective
the probability that a missile hit the target is 0.90. If three missile of this type has been fired. Find the probability that (i) at least 2 hit the target. (ii) Exactly two hit the target.
Events A and B of a probability space (Q,F,P) are independent. The probability that the both 3 and the probability that at least one event occurs is 25 17 . Determine P(A) occur is 25 and P(B).
Urn A has four red balls and two white balls, and urn B has three red balls and four white balls. A fair coin is tossed. If it lands heads up, a ball is drawn from urn A; otherwise, a ball is drawn from urn B. Compute (a) the probability a red ball is drawn (b) the probability that thecoin landed heads up, if it is known that a red ball was drawn.
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.
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A₁) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (Round your answers to four decimal places.) (a) What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period? (d) What is the probability that only the receiver needs service during the warranty period? (e) What is the probability that exactly one of the three components needs service…
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.
Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?
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
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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