A scientist is interested in two different types of particles; type A and type B. The time that it takes a particle of type A to decay can be modeled as an exponential distribution with a mean of 75 minutes, and the time that it takes for a particle of type B to decay can be modeled as an exponential distribution with a mean of 50 minutes. Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at which each of the particles decays is independent of all of the other particles in the container. (1) Calculate the probability that the first particle to decay is of type A. (2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the particles to decay, and the first particle that decays is of type B".
A scientist is interested in two different types of particles; type A and type B. The time that it takes a particle of type A to decay can be modeled as an exponential distribution with a mean of 75 minutes, and the time that it takes for a particle of type B to decay can be modeled as an exponential distribution with a mean of 50 minutes. Suppose that a container holds 10 particles; 7 of type A and 3 of type B. Assume that the rate at which each of the particles decays is independent of all of the other particles in the container. (1) Calculate the probability that the first particle to decay is of type A. (2) Calculate the probability of the following event; "it takes at least 30 minutes for any of the particles to decay, and the first particle that decays is of type B".
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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