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

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Manager
Status: Manager
Joined: 02 Nov 2018
Posts: 179
A traffic light runs repeatedly through the following cycle: green fo  [#permalink]

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15 Mar 2019, 22:32
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00:00

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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Manager
Joined: 12 Apr 2011
Posts: 148
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: A traffic light runs repeatedly through the following cycle: green fo  [#permalink]

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16 Mar 2019, 04:41
1
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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18 Mar 2019, 06:58
eabhgoy 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.
Re: A traffic light runs repeatedly through the following cycle: green fo   [#permalink] 18 Mar 2019, 06:58
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