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Consider you are travelling to International Islamic University H-10 Campus from Sector G-13 Islamabad via Srinagar Highway. Two traffic light signals were encountered on the Highway. The first signal is at G-11 while second signal is on Police Line. The outcome of each traffic signal is either red (r), yellow (y) or green (g). We can denote the outcome by a sequence of r and y such as ry, light at G11 signal is red followed by light at Police line signal is yellow. The events related to this experiment are Gı= {First signal is green}, Yı= {First signal is yellow}, RỊ= {First signal is red), G2= {Second signal is green}, Y2= {Second signal is yellow} and R2= {Second signal is red}. Assume that all outcomes are equally likely: a. Find P [G]], P [Y1], P [R1], P [G2], P [Y2] and P (R2]. b. Find the following probabilities: P [G/ G¡], P [Yz/ Y¡], P [R/ R¡], P [Gj/ G2], P (Y,/ Y2] and P (R1/ R2]. c. Are the events Gj and G2 are independent. Give reason for your answer as well. d. Are the events Y1 and Y2 are independent. Give reason for your answer as well. e. Are the events R1 and R2 are independent. Give reason for your answer as well.

Consider you are travelling to International Islamic University H-10 Campus from Sector G-13 Islamabad via Srinagar Highway. Two traffic light signals were encountered on the Highway. The first signal is at G-11 while second signal is on Police Line. The outcome of each traffic signal is either red (r), yellow (y) or green (g). We can denote the outcome by a sequence of r and y such as ry, light at G11 signal is red followed by light at Police line signal is yellow. The events related to this experiment are Gı= {First signal is green}, Yı= {First signal is yellow}, RỊ= {First signal is red), G2= {Second signal is green}, Y2= {Second signal is yellow} and R2= {Second signal is red}. Assume that all outcomes are equally likely: a. Find P [G]], P [Y1], P [R1], P [G2], P [Y2] and P (R2]. b. Find the following probabilities: P [G/ G¡], P [Yz/ Y¡], P [R/ R¡], P [Gj/ G2], P (Y,/ Y2] and P (R1/ R2]. c. Are the events Gj and G2 are independent. Give reason for your answer as well. d. Are the events Y1 and Y2 are independent. Give reason for your answer as well. e. Are the events R1 and R2 are independent. Give reason for your answer as well.

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...
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Consider you are travelling to International Islamic University H-10 Campus from Sector G-13 Islamabad via Srinagar Highway. Two traffic light signals were encountered on the Highway. The first signal is at G-11 while second signal is on Police Line. The outcome of each traffic signal is either red (r), yellow (y) or green (g). We can denote the outcome by a sequence of r and y such as ry, light at G11 signal is red followed by light at Police line signal is yellow. The events related to this experiment are Gı= {First signal is green}, Yı= {First signal is yellow}, Rı= {First signal is red}, G2= {Second signal is green}, Y2= {Second signal is yellow} and R2= {Second signal is red}. Assume that all outcomes are equally likely: a. Find P [G1], P [Yi], P [R1], P [G2], P [Y2] and P [R2]. b. Find the following probabilities: P [G/ Gj], P [Y2/ Y¡], P [R/ R¡], P [Gj/ G2], P [Y,/ Y2] and P (R1/ R2]. c. Are the events G1 and G2 are independent. Give reason for your answer as well. d. Are the events Yı and Y2 are independent. Give reason for your answer as well. e. Are the events Rị and R2 are independent. Give reason for your answer as well.
Transcribed Image Text:Consider you are travelling to International Islamic University H-10 Campus from Sector G-13 Islamabad via Srinagar Highway. Two traffic light signals were encountered on the Highway. The first signal is at G-11 while second signal is on Police Line. The outcome of each traffic signal is either red (r), yellow (y) or green (g). We can denote the outcome by a sequence of r and y such as ry, light at G11 signal is red followed by light at Police line signal is yellow. The events related to this experiment are Gı= {First signal is green}, Yı= {First signal is yellow}, Rı= {First signal is red}, G2= {Second signal is green}, Y2= {Second signal is yellow} and R2= {Second signal is red}. Assume that all outcomes are equally likely: a. Find P [G1], P [Yi], P [R1], P [G2], P [Y2] and P [R2]. b. Find the following probabilities: P [G/ Gj], P [Y2/ Y¡], P [R/ R¡], P [Gj/ G2], P [Y,/ Y2] and P (R1/ R2]. c. Are the events G1 and G2 are independent. Give reason for your answer as well. d. Are the events Yı and Y2 are independent. Give reason for your answer as well. e. Are the events Rị and R2 are independent. Give reason for your answer as well.
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