probability

Question

Manish has to travel from A to D changing buses at stops B and C enroute.The maximum waiting time at either stop can be 8 minutes each,but any time of waiting upto 8 minutes is equally likely at both places.He can afford upto 13 minutes of waiting time if he is to arrive at D on time,What is probability Manish will arrive late at D?

Answer 1

3/16 should be the correct answer.

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Maximum Possible Waiting Time = 8 + 8 = 16 mins.

Minimum Possible Waiting Time = 0 + 0 = 0 mins.

Given that, at both the stations B & C, any waiting time up to 8 minute is equally likely.

So any waiting time between 0 to 16 should be equally likely.

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Now the problem can be thought as "Choosing any point P randomly on real number line between 0 to 16(inclusive), what is the probability that the point will lie between 13 to 16."

Point P will represent our total waiting time, clearly all points will be equally likely since they will be equidistant from each other.

The Probability that P > 13 = length of line segment between 13 and 16 / length of line segment between 0 and 16

Hence the probability that total waiting time is greater than 13 minutes = (16 - 13) / (16 - 0) = 3/16

Manish will arrive late at D if he will spend more than 13 minutes in waiting.

So the probability that Manish will arrive late at D = 3/16.

Comments

Absolutely Wrong!!!! Ans Should be 9/128

Check this link for details--> https://math.stackexchange.com/questions/943046/travelling-from-one-destination-to-another

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3/16 is not there in option.

Answer 2

Ans should be 9/128. The Answer provided by Anurag Pandey is NOT right!

Check this link-----> https://math.stackexchange.com/questions/943046/travelling-from-one-destination-to-another