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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 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

Solution:

Given, a box contains 1000 sealed envelopes.

10 of them contain a cash prize of Rs. 100 each.

100 of them contain a cash prize of Rs. 50 each.

200 of them contain a cash prize of Rs. 10 each.

Rest do not contain any cash prize.

The box is well shuffled and an envelope is picked out.

We have to find the probability that the envelope contains no cash prize.

The probability of picking out an envelope that it contains no cash prize is given by

Favourable outcomes = Envelopes that do not contain cash prize

Envelopes that do not contain cash prize = total envelopes - envelopes that contain Rs. 100 - envelopes that contain Rs. 50 - envelopes that contain Rs. 10

= 1000 - 10 - 100 - 200

= 1000 - 310

= 690

Number of favourable outcomes = 690

Number of possible outcomes = 1000

Probability = number of favourable outcomes / number of possible outcomes

Probability = 690/1000

= 69/100

Therefore, the probability of selecting an envelope that contains no cash prize is 69/100.

✦ Try This: There are 100 sealed envelopes in a box, 10 of them contain a cash prize of Rs 50 each, 19 of them contain a cash prize of Rs 5 each and 20 of them contain a cash prize of Rs 10 each and 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?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 34

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 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

Summary:

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 rest do not contain any cash prize. If they are well shuffled and an envelope is picked out, the probability that it contains no cash prize is 69/100

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