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.

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Author:Jay Abramson
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Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
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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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