Q1) The inhabitants of an island tell the truth one third of the time. They lie with probability2/3. On an occasion, after one of them made a statement, you ask another 'was that statementtrue?' and he says 'yes'. What is the probability that the statement was indeed true?

Tell the truth one third of time P(True) = 1/3 They lie with probability 2/3 P(lie) = 2/3 We have…

Answered: Q1) The inhabitants of an island tell…

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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Suppose that your friend Kamala randomly chooses a number between 1 and 13 (including both 1 and 13) and asks you to guess what it is. Answer the following questions: 1. What is the probability she is thinking of an even number? 2. What is the probability the number she is thinking of has a 1 in it? 3. What is the probability that the number she is thinking of is at least 5? Suppose that Komala decides to tell you that the number she is thinking of is odd. Given that the number is odd, calculate the conditional probabilities below: 1. What is the probability she is thinking of an even number? 1. What is the probability the number she is thinking of has a 1 in it? 2. What is the probability that the number she is thinking of is at least 5?
The probability of happening of an event A is 0.5 and that of B is 0.3. if A and B are mutually exclusive events then probability of neither A nor B is
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3. Two coins are tossed 700 times, and the results are Two heads: 205 times One head: 325 times No head: 170 times Find the probability of each event to occur? 4. If P(A)-7/13, P(B)-9/13 and P(ANB)-4/13, evaluate P(A/B)? 5. Two dice are rolled, find the probability that the sum of the number of both the dice is: A.Equal to 2 B.Equal to 5 C.Less than 12 6. Let X be the number of Tell in four tosses of a fair coin a) Construct the Probability mass function (pf) of X. b) Find the mean number of Tell and the variance c) Find P(0 2. (i)Determine the corresponding p.d.f. (f(x)). (ii) Determine the constant c. 8. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value 9.Find the probability of getting at least 5 times head-on tossing an unbiased coin for 6 times by using the binomial distribution
Suppose that your friend Kamala randomly chooses a number between 1 and 13 (including both 1 and 13) and asks you to guess what it is. Answer the following questions: 1. What is the probability she is thinking of an even number? 2. What is the probability the number she is thinking of has a 1 in it? 3. What is the probability that the number she is thinking of is at least 5?
If you flip a coin 3 times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. What is the probability of getting at least one head? 3/4 O 7/8 O 1/4 O 1/2
21. A company in New Jersey is hiring 8 people for a position. Of the applicants, 10 are from New Jersey, 8 are from New York, and 7 are from Pennsylvania. What is the probability that of the 8 people hired, exactly 2 are from New Jersey, and what is the probability at least two are from New Jersey? Round off to 3 decimal places. _________ and ________

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Q1) The inhabitants of an island tell the truth one third of the time. They lie with probability 2/3. On an occasion, after one of them made a statement, you ask another 'was that statement true?' and he says 'yes'. What is the probability that the statement was indeed true?