Probability
Conditional probability; word arrangement
MMTS_Full_Test_19
Grade 12
Question:
The probability that in a random arrangement of the word MATHEMATICS, the two M's are not together given that the two A's are not together is
(A) $\dfrac{73}{90}$
(B) $\dfrac{36}{45}$
(C) $\dfrac{5}{6}$
(D) $\dfrac{37}{45}$
Step-by-Step Solution
Key Concept: Use conditional probability: $P(M\text{ sep}|A\text{ sep})=P(M\text{ sep}\cap A\text{ sep})/P(A\text{ sep})$. Count arrangements of MATHEMATICS letters carefully.
$P=\dfrac{37}{45}$.
Correct Answer: (D) $\dfrac{37}{45}$