Question

Out of the letters E, T, and N, a 3 letter word is formed using all the three letters. What is the probability that the word formed is TEN?

Answer 1

Hint: We can calculate the total number of 3 letter words formed using the given letters which will become our total number of outcomes and the number of times TEN can be formed will be the favorable outcomes. Then we can apply the formula of probability.
\[
  Probability(P){\text{ = }}\dfrac{{favourable{\text{ }}outcomes(f)\;}}{{total{\text{ }}outcomes(T)}} \\
  P = \dfrac{f}{T} \\
 \]

Complete step-by-step answer:
All 3 letter words that can be formed using ENT are:
ENT
ETN
NET
NTE
TEN
TNE
These are 6 words and will be the total outcomes for the probability.
Now,
Favorable outcomes (f) = occurrence of word TEN = 1
Total outcomes (T) = 6
Substituting the values in the formula of probability, we get :
\[
  P = \dfrac{f}{T} \\
  P = \dfrac{1}{6} \\
 \]
Therefore, out of the given letters, the 3 letter words are formed and the probability that the word formed is TEN is $\dfrac{1}{6}$ or 0.16

Note: The probability can be left either in fractions or can be converted to decimals.
The words that we wrote and the total number of possibilities in general is known as Sample Space.
The way of arranging letters should be letter wise assigning every possible position to respective letters so as to not get confused.
Probability is nothing but a possibility of an event to occur.
It lies between the range from 0 to 1 where 0 means that the event is impossible to occur and 1 means that the event will surely occur.