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Bunuel
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This question is a good candidate for calculated guessing. From 6:00 to 8:59, at least 1 hour out of the total 3 hours has a 8. So we are looking for a number more than 1/3 or 33%. Hence, options (a) and (b) are out. Options c,d and e translate to 40%, 44% and 50%. Since the number 8 appears very few times in a hour, option (c) must be our best guess.
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hi brunel,

i am unable to understand the point how digit 8 will appear 60 times from time interval 8:00 to 9:00.As per me 8:08 , 8:18 , 8:28 etc will give 8 6 times + 59 times on the hour digit.

kindly clear where i am going wrong

thanks in advance
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hi brunel,

i am unable to understand the point how digit 8 will appear 60 times from time interval 8:00 to 9:00.As per me 8:08 , 8:18 , 8:28 etc will give 8 6 times + 59 times on the hour digit.

kindly clear where i am going wrong

thanks in advance

The probability that he will see the digit 8, does not increase for 8:18, because there are two 8's there. It's still one point in time. Thus 8:18 is still counted once.
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The very best approach for this types of questions is an estimation. There are only 3 hours. The probability of seeing 8 is 1/3 plus another 12 cases. Slightly more than 1/3. 2/5 fits best.
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Another way to think about it:

3 hours between 6:00 and 9:00, 1/3 of those hours (from 8:00 - 8:59) you will definitely see an 8
Of the other two hours, the digit 8 is equally likely out of 10 digits to appear in the last digit.

So 1/3 + 2/3*1/10 = 2/5, Answer C
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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This is a pure probability approach if someone wants to dive directly into calculations as soon as you read the word probability.

Imagine three places to fill. _ _ _
Total Probability-
for 1st place - 3 ways to fill (6,7 or 8)
for 2nd place - 6 ways to fill (0 to 5)
for 3rd place - 10 ways to fill (0-9)
Total Probability = 3 * 6 * 10 = 180

Probability for 8 -
8 in 1st place, rest can be any numbers -
8 _ _
1 way (8) 6 ways (0-5) 10 ways (0-9) = 1*6*10 = 60
OR
8 in last place, rest can be any numbers (there is no case for 8 at 2nd place) -
_ _ 8
2 ways (6 or 7) 6 ways (0-5) 1 way (8) = 2*6*1 = 12
Probability for 8 = 60 + 12 = 72

Answer- 72/180 = 2/5

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Bunuel
An electronic clock displays time in hours and minutes. For instance, 08:15 represents a quarter past eight. If someone looks at the clock at a random time between 6:00 (inclusive) and 9:00 (exclusive) what is the probability that he will see the digit 8?

A. \(\frac{1}{5}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{4}{9}\)
E. \(\frac{1}{2}\)

Bunuel

Is below approach valid?

Probability of 8 on hour hand is 1/3, probability of 8 on minute hand is 12/180 not 18/180 as it will be repetition

1/3 + 12/180

= 72/180

2/5

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I did the same, my reasoning was: why would 8 appear more times than a 5 or 6? So I took 1/10 (1 out of 10 digits)*2 hours + 1hour/3= 2/5

However, I'm not sure if this reasoning could apply to other questions, as it is a sexagesimal system for time.

Bunuel, is this approach reasonable for these probability type of questions? Or it was a coincidence that I could get the correct answer?

Thanks in advance
siyeezy
Another way to think about it:

3 hours between 6:00 and 9:00, 1/3 of those hours (from 8:00 - 8:59) you will definitely see an 8
Of the other two hours, the digit 8 is equally likely out of 10 digits to appear in the last digit.

So 1/3 + 2/3*1/10 = 2/5, Answer C
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I did the same, my reasoning was: why would 8 appear more times than a 5 or 6? So I took 1/10 (1 out of 10 digits)*2 hours + 1hour/3= 2/5

However, I'm not sure if this reasoning could apply to other questions, as it is a sexagesimal system for time.

Bunuel, is this approach reasonable for these probability type of questions? Or it was a coincidence that I could get the correct answer?

Thanks in advance
siyeezy
Another way to think about it:

3 hours between 6:00 and 9:00, 1/3 of those hours (from 8:00 - 8:59) you will definitely see an 8
Of the other two hours, the digit 8 is equally likely out of 10 digits to appear in the last digit.

So 1/3 + 2/3*1/10 = 2/5, Answer C

From 6:00 to 6:59, the digit 6 appears in every number. The digit 0, 1, 2, 3, 4, and 5 appear in 15 numbers each. The digit 8 appears only 6 numbers. So, not all digits have an equal probability of appearing.
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I like the solution - it’s helpful.
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