Step 1: Analyze the word 'STATISTICS'
Total number of letters in 'STATISTICS' = 10
The frequency of each letter is:
Step 2: Analyze the word 'ASSISTANT'
Total number of letters in 'ASSISTANT' = 9
The frequency of each letter is:
Step 3: Identify the common letters
The letters common to both words are S, T, A, and I. For the chosen letters to be the same, they must both be one of these four letters.
Step 4: Calculate the probability for each common letter
Let P(X) be the probability of picking letter X from 'STATISTICS' and P′(X) be the probability of picking letter X from 'ASSISTANT'.
-
For letter 'S':
-
For letter 'T':
-
For letter 'A':
-
For letter 'I':
Step 5: Calculate the total probability
The total probability is the sum of the probabilities of these mutually exclusive cases:
P(Same Letter)=P(S,S)+P(T,T)+P(A,A)+P(I,I)
P(Same Letter)=909+906+902+902
P(Same Letter)=909+6+2+2=9019
Conclusion:
The probability that the two letters taken at random are the same is 19/90.
Correct Option: (c)
