4.41. A fair die is tossed. Consider events A = {1,3,5}, B = {2,3,5}, C = {1,2,3,4}. Find:(a) P(AB) and P(A U C)(b) P(A/B) and P(BA)(c) P(AIC) and P(CIA)

A fair die is tossedTotal no. of outcomes=6 (i.e.,…

Answered: A fair die is tossed. Consider events A…

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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3a) Luis is applying for admission to a University. He must complete a written application, and then be interviewed by the admission committee. The probability of being approved on the written application is 0.60. The probability of being approved by the interview committee given the candidate was approved on the written application is 0.70. What is the probability Luis is approved on both the written application and the interview? P(A and B) 3b) Professor Wan is preparing students for the entrance test at Bronx Community College. Records show that 75% of the students need work in math, 60% need work in English, and 50% heed work in both areas. What is the probability that a student selected at random needs math or need English? P(A DRB)=
Photos and videos have become an important part of the online social experience, with more than half of Internet users posting photos and videos online that they have taken themselves. Let A be the event an Internet user posts photos that he or she has personally taken, and B be the event an Internet user posts videos that he or she has personally taken. Pew Research Center finds that P(A) = 0.52, P(B) = 0.26, and P(A or B) = 0.54. What is the conditional probability that an Internet user posts photos that he or she has personally taken, given that he or she posts videos that he or she has personally taken? (Enter your answer rounded to three decimal places.) Р(A | В) —D
Given two events A and B such that P (A) = 1/2 and P (B) = 1/3. Determine P (B | A) if (a) A and B are disjoint. (b) P (A \ B) = 1/6
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14. Event A and Event B are dependent. 21 a) P(B)=; p(A and B) 200 P(B|A) = b) P(B|A) = ; P(A and B) P(B) = 200
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
Determine if events A and B are independent. 7 P(A and B) 20 7 13 P(B) : 20 13 P(A and B) 20 169 4) = P(B) = 2) P(A) = 100 400 7 3) Р(A) %—D 10 P(B) = 5 21 1 P(B) 1 P(A and B) 5 1 P(A and B) 4) Р(A) — 100 25
3 2 1. Given that P(4)=, P(A/ B)= and P(A/B)=. find : P(ANB) P(B) P(AUB) (а) (i) (ii) (iii) (b) Determine whether the events A and B are : (i) (ii) Mutually exclusive Independent (c) Given that P(A)=0.64 , P(B)=0.36 and P(BnA)= 0.25. Find : (i) P(AOB) (ii) P(AUB) (iii) P(BnA)
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.

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A fair die is tossed. Consider events A = {1,3,5}, B = {2,3,5}, C = {1,2,3,4}. Find: (a) P(AB) and P(AUC) (b) P(A/B) and P(BIA) (c) P(A/C) and P(CIA)