Homework Help is Here – Start Your Trial Now!
Math
Probability
Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)- P(BnC)+ P(An BnC). that whenever events A, B, C are mutually independent, we have that P(AUBUC) =1- P(A°)P(B°)P(C®) = 1 – (1 – P(A)) · (1 – P(B))· (1 – P(C)) he probability in question can be calculated considerably faster than with the use of the formula (4.1)). The probability that A hits a target is 1/6, the probability that B hits it is 4/7. and the probability that C hits th

Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An B) – P(AnC)- P(BnC)+ P(An BnC). that whenever events A, B, C are mutually independent, we have that P(AUBUC) =1- P(A°)P(B°)P(C®) = 1 – (1 – P(A)) · (1 – P(B))· (1 – P(C)) he probability in question can be calculated considerably faster than with the use of the formula (4.1)). The probability that A hits a target is 1/6, the probability that B hits it is 4/7. and the probability that C hits th

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Question
1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B) + P(C) – P(An B) – P(AnC) – P(BNC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC)= 1– P(A°)P(B°)P(C°) = 1- (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 1/6, the probability that B hits it is 4/7, and the probability that C hits the target is 2/5. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p> 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1– p)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0007 and n = 500, and then round your result to a 5-digit floating-point number. You may not include the proof of the result in (i) in your table with the answers (but do try to obtain the proof, and keep it for your records).
Transcribed Image Text:1. (Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B) + P(C) – P(An B) – P(AnC) – P(BNC) + P(AN BnC). (4.1) Prove that whenever events A, B,C are mutually independent, we have that P(AUBUC)= 1– P(A°)P(B°)P(C°) = 1- (1– P(A)) · (1 – P(B)) · (1 – P(C)) (and the probability in question can be calculated considerably faster than with the use of the formula (4.1)). (ii) The probability that A hits a target is 1/6, the probability that B hits it is 4/7, and the probability that C hits the target is 2/5. Use (i) to find the probability that the target will be hit if A, B, and C each shoot at the target. (iii) Suppose that the probability that a soldier firing his personal weapon hits an enemy warplane is p> 0. Show then, arguing as in (i), that the probability that the warplane is hit at least once when n > 2 soldiers shoot at it is 1- (1– p)". (4.2) Evaluate the probability in (4.2) in the case when p = 0.0007 and n = 500, and then round your result to a 5-digit floating-point number. You may not include the proof of the result in (i) in your table with the answers (but do try to obtain the proof, and keep it for your records).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS