What is the probability that the
minute and hour hands of a clock will
form an acute angle at any given time?
Answers
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Given:
Minute hand and hour hand
To Find:
Probability that the minute and hour hands of a clock will form an acute angle.
Solution:
1) Suppose hour hand fixed at 12
2) Now acute angle is possible when minute hand is between 9 to 3 & there is exactly ½ possibility that the minute and hour hands of a clock will form an acute angle because we get the same angle for the interval of 9 to 3 and 3 to 9 again.
3) In this case we supposed that hour hand is at 12, you can suppose at anywhere, possibility of getting acute angle will be constant (½) will be constant for the every case so on the average we get the probability as 1/2.
So the probability that the minute and hour hands of a clock will form an acute angle is 1/2.
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