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A traffic light runs repeatedly through the following cycle: green fo

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A traffic light runs repeatedly through the following cycle: green fo  [#permalink]

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New post 15 Mar 2019, 22:32
2
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

46% (02:42) correct 54% (03:02) wrong based on 24 sessions

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A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?

(A)\(\frac{1}{63}\)

(B)\(\frac{1}{21}\)

(C)\(\frac{1}{10}\)

(D)\(\frac{1}{7}\)

(E)\(\frac{1}{3}\)

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Re: A traffic light runs repeatedly through the following cycle: green fo  [#permalink]

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New post 16 Mar 2019, 04:41
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Noshad wrote:
A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?

(A)\(\frac{1}{63}\)

(B)\(\frac{1}{21}\)

(C)\(\frac{1}{10}\)

(D)\(\frac{1}{7}\)

(E)\(\frac{1}{3}\)


So here we have a 63 seconds cycle:

1) 0-30 seconds: Green
2) 31-33: Yellow
3) 34-63: Red

and then it starts again

Now we need to focus on 3 seconds intervals in which the light changes colour. Following are such intervals:

1) 28-29-30
2) 29-30-31
2) 30-31-32

4) 31-32-33
5) 32-33-34
6) 33-34-35

7) 61-62-63
8) 62-63-64
9) 63-64-65

Hence every 63 seconds we will have 9 such instances

Hence Probability = (No of favourable outcomes)/(Total number of outcomes) = 9/63 = 1/7

Hence D is the correct answer.
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Re: A traffic light runs repeatedly through the following cycle: green fo  [#permalink]

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New post 18 Mar 2019, 06:58
eabhgoy wrote:
Noshad wrote:
A traffic light runs repeatedly through the following cycle: green for 30 seconds, then yellow for 3 seconds, and then red for 30 seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while she is watching?

(A)\(\frac{1}{63}\)

(B)\(\frac{1}{21}\)

(C)\(\frac{1}{10}\)

(D)\(\frac{1}{7}\)

(E)\(\frac{1}{3}\)


So here we have a 63 seconds cycle:

1) 0-30 seconds: Green
2) 31-33: Yellow
3) 34-63: Red

and then it starts again

Now we need to focus on 3 seconds intervals in which the light changes colour. Following are such intervals:

1) 28-29-30
2) 29-30-31
2) 30-31-32

4) 31-32-33
5) 32-33-34
6) 33-34-35

7) 61-62-63
8) 62-63-64
9) 63-64-65

Hence every 63 seconds we will have 9 such instances

Hence Probability = (No of favourable outcomes)/(Total number of outcomes) = 9/63 = 1/7

Hence D is the correct answer.


Well I think there is a huge probability of getting this question incorrect :P
while i was solving it, I didn't consider that the light would change during above underlined time intervals. I hope u get the reason why.
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Re: A traffic light runs repeatedly through the following cycle: green fo   [#permalink] 18 Mar 2019, 06:58
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