Exercise 3.42 Let N be the number of the events A1, A2,., An which occur. Show thatE(N) = >P(A;).i=1

Given : Let N be the number of events A1 , A2 , ......,An which occurs. Our aim is to show that

Answered: Let N be the number of the events A1,…

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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LO1,2, 31Q1. (22 points)] This question consists of 11 paragraphs. In each part, circle the correct answer. 1. Let A and B be two events such that Ac B, then P(4B)= a. P(A) b. P(4) c. P(B) d. 0 e. None 2. How many different four-digit numbers can be formed from the digits 1, 2, 3, 4, 5,6,7 such that the first digit 3 or 6 also you cannot repeat the digit. a. 240 b.48 c. 120 e. None 3. If A, B and C are mutually independent events and that P(A)= 0.3, P(B) = 0.2, P(C)=0.4. The probability that at least one of the events occur is b.0.664 a. 0.336 e. 0.024 d. 0.976 e. None 4. A box contains 3 red balls and 5 black balls. Balls are drawn randomly one at a time with replacement from the box. The probability that the third red ball is the seventh ball drawn is. a. 0,169 b.0.282 c. 0.179 d. 0.121 e. None 5. A box contains 20 balls, 13 of them are red and the rest are blue. Three balls are drawn randomly without replacement. The probability of getting at least 1 blue ball is. a) 0.749 b) 0.251…
An integer is chosen at random from tle first two lundred digits. What is the probability that the integer closen is divisible by 6 or 8 ?
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8. Let A, B be two events with P(A) = ½, P(A − B) = 3, determine P(AB).
1. Let A and B be two events such that ACB, then P(AB)= 1,2,3/Q1. (22 points)] This question consists of 11 paragraphs. In each part, circle the correct an a. P(A) d.0 b. P(A) c. P(B) 2. How many different four-digit numbers can be formed from the digits 1,2,3,4,5,6,7 such that the first digit 3 or 6 also you cannot repeat the digit. a. 240 b.48 c. 120 3. If A, B and C are mutually independent events and that P(A) = 0.3, P(B) = 0.2, P(C) = 0.4. The probability that at least one of the events occur is a. 0.336 c. 0.024 b.0.664 d. 0.976 e. None 4. A box contains 3 red balls and 5 black balls. Balls are drawn randomly one at a time with replacement from the box. The probability that the third red ball is the seventh ball drawn is. a. 0.169 b.0.282 c. 0.179 d. 0.121 e. None 5. A box contains 20 balls, 13 of them are red and the rest are blue. Three balls are drawn randomly without replacement. The probability of getting at least I blue ball is. a) 0.749 b) 0.251 c) 0.479 d) 0.521 a. 0.4 b.…
Q/C/ If the disjoint events A and B such that P(B)=1/3 , then the value of P(Bn A) is------.
A number is chosen randomly from the first 25 natural numbers (1 to 25). If event A={a multiple of 4), what is the value of P(A')? Write you answer in decimal form.
The area where events A and B overlap is O A and B O A and B' O A' and B' O A or B to search 12 F3 F4 F5
2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
5.3 A bent coin, with heads probability .2, is tossed 13 times. Let X be the number of heads in the 13 tosses. Find (a) P(X =5), and (b) P(X = 12).
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Let N be the number of the events A1, A2,..., An which occur. Show that n E(N) = P(A;). i=1