# The cards bearing letters of the word “MATHEMATICS” are placed in a bag. A card is taken out from the bag without looking into the bag (at random).

(a) How many outcomes are possible when a letter is taken out of the bag at random?

(b) What is the probability of getting (i) M? (ii) Any vowel? (iii) Any consonant? (iv) X?

**Solution:**

Given, the cards bearing letters of the word “MATHEMATICS” are placed in a bag.

A card is taken out from the bag without looking into the bag at random.

(a) We have to find the number of possible outcomes when a letter is taken out of the bag at random.

Number of letters in the given word is 11.

So, there are 11 cards each representing the letters of the given word.

Possible outcomes = M, A, T, H, E, M, A, T, I, C, S

Number of possible outcomes = 11

Therefore, the number of possible outcomes is 11.

(b) Possible outcomes = M, A, T, H, E, M, A, T, I, C, S

Number of possible outcomes = 11

__Probability__ = Number of outcomes favourable to the event/Total number of outcomes in the experiment

(i) We have to find the probability of getting M.

Favourable outcomes = M, M

Number of favourable outcomes = 2

Probability of getting M = 2/11

(ii) We have to find the probability of getting any vowel.

Favourable outcomes = A, E, A, I

Number of favourable outcomes = 4

Probability of getting any vowel = 4/11

(iii) We have to find the probability of getting any consonant.

Favourable outcomes = M, T, H, M, T, C, S

Number of favourable outcomes = 7

Probability of getting any consonant = 7/11

(iv) We have to find the probability of getting x.

Favourable outcomes = 0

Number of favourable outcomes = 0

Probability of getting any consonant = 0/11

**✦ Try This: **The cards bearing letters of the word “TRANSVERSAL” are placed in a bag. A card is taken out from the bag without looking into the bag (at random). How many outcomes are possible when a letter is taken out of the bag at random

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 3

**NCERT Exemplar Class 7 Maths Chapter 3 Sample Problem 11**

## The cards bearing letters of the word “MATHEMATICS” are placed in a bag. A card is taken out from the bag without looking into the bag (at random). (a) How many outcomes are possible when a letter is taken out of the bag at random? (b) What is the probability of getting (i) M? (ii) Any vowel? (iii) Any consonant? (iv) X

**Summary:**

The cards bearing letters of the word “MATHEMATICS” are placed in a bag. A card is taken out from the bag without looking into the bag (at random), (a) The number of possible outcomes when a letter is taken out of the bag at random is 11, (b) The probability of getting (i) M is 2/11, (ii) Any vowel is 4/11, (iii) Any consonant is 7/11, (iv) X is 0/11

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