Probability of Matching Times on a ClockDate: 09/14/2004 at 12:17:07 From: Michael Subject: What is the probablity What is the probability of two different times within the same hour ending in the same last digit? Like 08:13 and 08:43? I don't know the process of calculating the probability. Date: 09/14/2004 at 12:59:58 From: Doctor Edwin Subject: Re: What is the probablity Hi, Michael. In general, the chance of an event occurring is # of ways the event could happen -------------------------------------- total # of ways things could turn out So for example my chance of rolling a one or a two on a six-sided die is: # of ways I could roll 1 or 2 --------------------------------------- total # of ways the die could come up or: 2 --- 6 which is just 1/3. Your question has an interesting twist. The most obvious answer is 1/10 or 10%. Let's ignore everything but the last digit. If I pick a number between zero and nine, and you do the same, the chance that you picked the same number I did is 1/10. So if I pick a time at random, and you pick a time at random, the chance that the last digits will match is still 1/10. But in your problem, it adds two additional pieces of information. First, it says that the times must be different. So we can't both pick 8:13, for example. The other piece is that the two times must fall within the same hour. In order to figure out the probability of your time event, we have to figure out how many ways we could have the same number at the end, while picking DIFFERENT times in the same hour. Suppose like in your example I pick 8:13. Now, how many ways can you pick a time that ends with the same digit as mine? 8:03 8:13 8:23 8:33 8:43 8:53 but one of those is the same time I picked, and you're not allowed to pick that one, so you're down to 5 possible ways to pick the time. So your probability is 5 ---------------------------------------- total # of times you could have picked So how many times could you have picked? There are 60 minutes in an hour, and you're not allowed to pick one of them. Can you figure out the probability from there? Write back if you're stuck. - Doctor Edwin, The Math Forum http://mathforum.org/dr.math/ |
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