Question

If one letter is chosen at random from the word 'mathematics'. Find the probability of choosing:
(a) 'm' alphabet
(b) 'a' alphabet
(c) 'c' alphabet

Answer 1

'MATHEMATICS'

$M\to 2$

$A\to 2$

$T\to 2$

$H\to 1$

$E\to 1$

$I\to 1$

$C\to 1$

$S\to 1$

a) 'm' alphabet

$p\left(m\right)=\frac{{}^2{C}_1}{{}^{11}{C}_1}=\frac{2}{11}$

b) 'a' alphabet

$p\left(a\right)=\frac{{}^2{C}_1}{{}^{11}{C}_1}=\frac{2}{11}$

c) 'c' alphabet

$p\left(c\right)=\frac{1}{11}$.