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Q.

There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each, and 200 of them contain a cash prize of Rs 10 each and the rest do not contain any cash prize. If they are well shuffled and an envelope is picked out, what is the probability that it contains no cash prize?

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a

\frac{69}{100}

b

\frac{2}{100}

c

\frac{26}{100}

d

\frac{20}{910}

answer is A.

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Detailed Solution

It is given that the total number of sealed envelopes is 1000.
The number of boxes contains a cash prize of Rs. 100 each is 10. The number of boxes contains a cash prize of Rs. 50 each is 100. The number of boxes containing a cash prize of Rs. 10 each is 200.
Let us assume that P(E) is the probability of an event “E”, n(S) is the total number of events in the sample space and n(E) is the number of favorable outcomes.
The total number of sealed envelopes in a box is

n S = 1000

.

No . of envelopes containing cash prize = 10 + 100 + 200 = 310

No . of envelopes containing no cash prize = 1000 − 310 = 690

So we have

n (E) = 690 .

The probability that the envelopes containing no cash prize:
Question Image

\Rightarrow \frac{690}{1000}

\Rightarrow 0.69

The probability that the envelopes containing no cash prize are 0.69.
Therefore, 1 is the correct answer.

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