Probability Question

Question

An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ?

The answer to this question is 2/5 arrived thus: 72 minutes with 8 in display, a total of 180.

My question is if I added all the numbers in display between 600 and 900 (inclusive) then I get 181 total. For example
600-659 - 60 #s
700-759 - 60 #s
800-859 - 60 #s
900 - 1 #
Total 181 of which there are 6 in the first group, 6 in the second group and 60 in the third that have 8 in display. So should not the probability be 72/181?

gurpreetsingh · Answer

IMO probability should be 72/180

600-659 - 60 #s
700-759 - 60 #s
800-859 - 60 #s
900 -  0  #

Read the question in red, it said time in between 6-9 that means we should exclude the case 9:00.
The person will start at 6:00 and end at 8:59. He does not look at the 9:00 value.

mainhoon · Answer

Well gurpreetsingh, what I don't understand is if I said between X and Y (and meant neither is inclusive) I should treat both the same, meaning if I exclude Y I also exclude X. In this case I then should exclude 600 and 900 so the total is now 179, why retain 600 and exclude 900?

gurpreetsingh · Answer

Yar, dont mind but I have seen in many of your posts, you give more emphasis on solving the question rather than learning from it I might be wrong but I cant resist myself pointing out something. :-D This problem is little ambiguous and might not appear on the exam. If you read my previous post again I have clearly mentioned that "Read the question in red, it said time in between 6-9 that means we should exclude the case 9:00. The person will start at 6:00 and end at 8:59. He does not look at the 9:00 value." He will start at 6:00:00 , at 6:00:01 ( here 01 are secs) he will still see 6:00 on the digital clock. This will be continued till 8:59:59. As he will look at the clock between 6:00 and 9:00, he still has 60 secs post 6:00 to consider 6:00 case. This is the reason 6:00 is included and 9:00 is not. PS: Don't mind for my harsh words, that's my way to motivate people.

If you are not able to understand anything, you are always welcome. But I advice you to spend some time,even an hour to know your doubt. Learning from own mistakes is the best way to learn.

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