Direction: Given a binomial random variable X with n = 25 andp = 0.60, find the following probabilities: , .(a) P(X< 10)(b) P(x2 12)(c) P(18

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Answered: Direction: Given a binomial random…

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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Ahmed recently caught Covid-19. He had contact to 7 persons. Let X be the number of persons he infected, a discrete random variable. The probability distribution of X is as follows: 1 2 3 4 7 P(X) 0.079 0.203 0.079 0.118 0.28 0.021 0.01 0.21 Find the following probabilities (in 3 decimal places): (a) What is the probability that he infected more than 3 persons? (b) What is the probability that he infected 8 persons? (c) What is the probability that he did not infect anybody?
A news company reported that 7% of adult Americans have a food allergy. Consider selecting 10 adult Americans at random. Define the random variable x as x = number of people in the sample of 10 that have a food allergy. Find the following probabilities. (Round your answers to three decimal places.) (a) P(x < 2) (b) P(x ≤ 2) (c) P(x ≥ 3) (d) P(1 ≤ x ≤ 2)
The PMF of the number of components K of a system that fails is defined by = {( PK (k)= ()(0.2)*(0.8) 4-k k= 0, 1,...,4 otherwise (a) What is the CDF of K? (b) What is the probability that fewer than two components of the system fail?
In a digital communication channel, assume that the number of bits received in error can be modeled by a binomial random variable, and assume that the probability that a bit is received in error is 0.0001. If 150,000 bits are transmitted, what is the probability that errors are between 10 and 18? How to compute P(X=10)= (150000c10)(0.0001)10(1-0.0001)150000-10
The prior probabilities for events A1 and Ag are P(A1) = 0.50 and P(A2) = 0.50. It is also known that P(A n A2) = 0. Suppose P(B|A1) = 0.10 and P(B|A2) = 0.70. a. Are events Aj and Ag mutually exclusive? Yes Explain. (i) P(A1 N A2) = 0 (ii) P(A1) + P(A2) = 1 (iii) P(A2) + P (A2 | A1) (iv) P(A2) + P(A2 | A1) choice (i) b. Compute P(A1 n B) (to 2 decimals). 0.165 Compute P(A2 N B) (to 2 decimals). 0.4819 c. Compute P(B) (to 2 decimals). 0.415 d. Apply Bayes' theorem to compute P(A1|B) (to 4 decimals). Also apply Bayes' theorem to compute P(A2|B) (to 4 decimals).
A binomial experiment for the random variable X was performed with 10 trials. The probability of success was found to 0.44. Determine the following probabilities: [Round to four decimal places.] a.) P(X = 4)= b.) P(X 6) =
Which of these is not a probability? (a) 230% (b) 2/3 (c) . 23232323 (d) 2.3% (e) 2:3
A news company reported that 6% of adult Americans have a food allergy. Consider selecting 15 adult Americans at random. Define the random variable x as x = number of people in the sample of 15 that have a food allergy. Find the following probabilities. (Round your answers to three decimal places.) (a) P(x < 2) (b) P(x ≤ 2) (c) P(x ≥ 3) (d) P(1 ≤ x ≤ 2) You may need to use the appropriate table in the appendix to answer this question.
A news company reported that 7% of adult Americans have a food allergy. Consider selecting 15 adult Americans at random. Define the random variable x as x = number of people in the sample of 15 that have a food allergy. Find the following probabilities. (Round your answers to three decimal places.) (a) P(x < 2) (b) P(x ≤ 2) (c) P(x ≥ 3)
I need answer for P(x=3) and correct answer for the mean
Q5: The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker? (A) 5/8 (В) 1/2 (C) 1/5 (D) None of the above Q6: The probability that a person owns a microwave oven is 0.70, that a person owns a CD player is 0.26, and that person owns both a microwave and a CD player is 0.16, then the probability that a person owns a microwave or a CD player is (A) 0.5 (B) 0.182 (C) 0.8 (D) None of the above
2. A random variable|x has the following probability distribution. Find the value of p and then evaluate the following probabilities: P(X 5) and P(0 < X < 6). Find the mean of the probability distribution. 1 3 4 6 17 P(X) 2p 2p 3p p2 2p2 7p? + p Value of p = P(X < 5) =. P(X 2 5) = P(0 < X < 5) = Mean (u) =

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Direction: Given a binomial random variable X with n = 25 and p = 0.60, find the following probabilities: ,. (a) P(X< 10) (b) P(X>12) (c) P(18