Probability
Conditional probability; word arrangement
Grade Class 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
$\dfrac{73}{90}$
$\dfrac{36}{45}$
$\dfrac{5}{6}$
$\dfrac{37}{45}$
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: 4