Question

A box contains letters, shown as MARCHING. What is the probability of the outcome in that order if letters are drawn one by one (a) with replacement? (b) without replacement?

Answer 1

There are 8 letters in the word MARCHING.

So, the number of letters in the box, N=8

b)

The probabilty of drawing the first letter M is,

`P(M)=(1)/(N)=(1)/(8)`

If the letter is not replaced, the number of remaining letters in the box is 7.

So, the probabilty of drawing the second letter A is,

`P(A)=(1)/(7)`

Similarly, the probabilities of drawing letters R,C,H,I, N and G respectively is,

`\begin{gathered} P(R)=(1)/(6) \\ P(C)=(1)/(5) \\ P(H)=(1)/(4) \\ P(I)=(1)/(3) \\ P(N)=(1)/(2) \\ P(G)=1 \end{gathered}`

So, the probability of of the outcome in that order if letters are drawn one by one​ without replacement is,