Conditional on B the events A1,..., A11 are independent with probability 0.8 each. The con-ditional probability that a particular collection of eight programs out of the 11 will compile is0.880.23 = 0.001342. There are165 different such collections of eight programs out of the11, so the probability of exactly eight programs will compile is

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Answered: Conditional on B the events A1,..., A11…

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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In the spreading of a rumour, each person who is told the rumour has probability p of believing it and only those who believe the rumour will pass it on. Assume that all individuals behave independently of each other and the rumour is never told to someone who has already heard it. Assume also that each person who is told the rumour and believes it on the n-th day will pass the rumour on to two other people on the (n + 1)-st day. Suppose that the rumour originates on day 1 from a single individual telling the rumour to two other people. Let Zo = 1 and for n ≥ 1 denote by Z₁, the number of people who are told the rumour on day n and believe it. (i) Explain why (Zn)nzo is a branching process. (ii) Find the probability mass function and the probability generating function of Z₁. (iii) What is the probability that the spread of the rumour ultimately ceases? (iv) For what values of p is the spread of the rumour certain to cease eventually? (v) For n ≥ 1 show that P(Zn = 2") = p2¹ +22+ +2″
A store has 12 cars for sale. 5 are new, 4 are accident cars and 3 are used but in good condition. If 3 cars are selected at random for shipping to a customer. Let X be the number of new cars in the shipment. If a customer wants one new car, one accident car and one used car. In how many ways can this selection be done? Find the probability function for X.
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: A tail on both the first and the last tosses Event B: A tail on the first toss or the second toss (or both) Event C: Alternating head and tail (with either coming first) THT TTT 0 O O O O TTH O O O Outcomes HHT O 0 O THH HTT U U O O O O HTH O O O HHH U O U Probability 0 0 010 믐
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: Two or more tails Event B: Exactly one head Event C: A tail on both the first and the last tosses TTT HHH 0 HTT Outcomes THT HHT HTH TTH THH Probability 0 0 0 5 ? DZ A 8 >
The month of September has thirty days. It is found on average that rain falls on twelve out of the thirty days in September. Assuming that it is equally likely that rain falls on any day in September, the probability that in any seven day period the first two days will be wet and the next five days will be dry is:
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.

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