Question

What is the probability of choosing the letter a from the word mathematics?

Answer 1

There are 11 letters in MATHEMATICS which consist of 2 each of M, A and T and 1 each of H, E, I, C and S.  

 

P(M on 1st choice) = 2/11   since there are 2 M's out of 11 letters

P(A on 2nd choice) = 2/10   since there are 2 A's out of 10 remaining letters

P(T on 3rd choice) = 2/9     since there are 2 T's out of 9 remaining letters

 

At this point there are 8 letters remaining which are all distinct so they must be chosen in the correct order 

 

P(H on 4th choice) = 1/8

P(E on 5th choice) = 1/7

P(M on 6th choice) = 1/6

P(A on 7th choice) = 1/5

P(T on 8th choice) = 1/4

P(I on 9th choice) = 1/3

P(C on 10th choice) = 1/2 

P(S on 11th choice) = 1/1  

 

The probability of spelling the word correctly is the product of all the probabilities 

 

P = 2*2*2 / 11! = 8 / 39916800 = 1 / 4989600 ~ 2 x 10-7 

Answer 2

Answer:

$\frac{2}{11}$

Step-by-step explanation:

To Find: Probability for choosing letter 'A' in 'MATHEMATICS'.

Concept: $P(A) = \frac{n(A)}{n(S)}$

Where,

• P(A) is the probability of an event “A”

• n(A) is the number of favorable outcomes

• n(S) is the total number of events in the sample space

Solution: According the question,

No. of occurrences of letter 'A' in 'MATHEMATICS' [n(A)] = 2  

Total no. of letters in 'MATHEMATICS' [n(S)] = 11

Then,

Probability for choosing letter 'A' in 'MATHEMATICS' [P(A)] = $\frac{n(A)}{n(S)}$

⇒ $\frac{2}{11}$

∴ Probability for choosing letter 'A' in 'MATHEMATICS' is $\frac{2}{11}$

#SPJ2