A box of 100 gaskets contains 10 gaskets with Type A defects, 5 gaskets with Type B defects and 2gaskets with both type of defects. Find the probabilities that:(i) A gasket to be drawn has type B defect under the condition that it has a type A defect.(ii) A gasket to be drawn has no type B defect under the condition that it has no type A defect.

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Answered: A box of 100 gaskets contains 10…

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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Urn A contains x red marbles and y white marbles, and urn B contains z red marbles and v white marbles. (i) If an urn is selected at random and a marble drawn, what is the probability that the marble is red? (ii) If a marble is drawn from urn A and put into urn B and then a marble is drawn from urn B, what is the probability that the second marble is red?
There are two bags containing several colored balls. The bag B, contains 10 red balls, 12 blue balls, and 13 green balls. The bag B, contains 20 red balls, 19 blue balls and 19 green balls. A student of your class wanted to draw 1 red ball and 3 blue balls. i. If he has the option to draw from only bag B1, what is the probability of drawing the four balls? [Give your answer upto 4 decimal places] ii. If he can choose any bag in an equiprobable manner, what is the probability of drawing the four balls in this case? [Give your answer upto decimal places] 4
Consider two urns: Urn-1 contains 3 red, 2 black and 4 white balls while Urn-2 contains 4 red, 4 black and 3 white balls. An urn is randomly selected with equal chances of it being Urn-1 or Urn-2, and then a ball is picked at random from the selected urn. (a) Find the probability that either a white or a red ball is picked? Your answer correct up to four decimal places. (b) If the picked ball is NOT black, find the probability it came from Urn-2? Your answer correct up to four decimal places.
A nuclear reactor becomes unstable if both safety mechanisms A and B fail. The probabilities of failure are P(A) =1/300 and P(B) = 1/200. Also, if A has failed, B is then more likely to fail: P(B/A)=1/100. a) What is the probability of the reactor going unstable? b) If B has failed, what is the probability of the reactor going unstable?
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
1. A class of 18 pupils consist of 11 girls, 4 of whom are left-handed, and 7 boys, only one of whom is left-handed. The two pupils are to be chosen at random from the class to act as monitors. Calculate the probabilities that the chosen pupils will consist ofa. One girl and One boyb. One girl who is left-handed and one boy who is left-handedc. Two left-handed pupils
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
first 2 parts please
At the local supermarket, out of the 100 cartons of eggs on sale, 8 have at least one egg inside that has cracked. If two cartons are chosen at random from the 100 without replacement, find the probabilities of: (a) Neither cartons having a cracked egg inside. (b) Both cartons having at least one cracked egg inside. (c) One carton not having a cracked egg inside, while the other having at least one cracked egg inside. Please answer all.
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
A university computer laboratory installs one of three operating systems on each computer used in the lab. It is known from product testing that during an hour of web browsing the probability a computer with system 1 installed will crash is 0.15, the probability of a computer with operating system 2 crashing is 0.08 and the probability of a computer with system 3 crashing is 0.1. Operating systems 1 and 3 are installed on the same number of computers while system 2 is installed on twice as many computers as system 1 (or system 3).a) What is the probability that a randomly selected computer crashes during an hour of web browsing?b) If a computer selected at random crashed during an hour of browsing the web, what is the probability it has operating system 2 installed?c) If a computer selected at random does not crash during an hour of web browsing what is the probability it has operating system 1 or operating system 2 installed?

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