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Question

A sum of money is rounded off to the nearest rupee. The probability that the round off error is at least ten paise is


A

79100

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B

80100

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C

81100

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D

None of these

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Solution

The correct option is C

81100


Explanation for the correct option:

Step 1: According to the question.

The sample space is the total outcomes for this situation are all possible errors in rounding off to the nearest rupee are

S={-0.50,-0.49,-0.48,........,-0.01,0.00,0.01,0.02,.....,0.49}

When we add all these samples, we get

n(S)=100

Let E be the event that the round off error is at least 10 paisa

Let E' be the event for the round off error not more than 9 paisa is

E'=-0.09,-0.08,-0.07,..........,-0.01,0.00,0.01,0.02,......,0.09

When we add all these events, we get the favorable outcomes as

n(E')=19

Step 2: Finding the probability

Probability that the round off error is not more than 9 paisa is

P(E')=19100

Thus the probability that the round off error is at least 10 paisa is

P(E)=1-P(E')=1-19100=81100

Hence, option (C) 81100 is the correct answer.


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