COMEDK · Maths · 36. Probability
If a number \(n\) is chosen at random from the set \(\{11,12,13, \ldots \ldots, 30\}\). Then, the probability that \(n\) is neither divisible by 3 nor divisible by 5, is
- A \(\dfrac{13}{20}\)
- B \(\dfrac{9}{20}\)
- C \(\dfrac{7}{20}\)
- D \(\dfrac{11}{20}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{11}{20}\)
Step-by-step Solution
Detailed explanation
The set of numbers is \(S = \{11, 12, 13, \ldots, 30\}\). The total number of elements in \(S\) is \(30 - 11 + 1 = 20\). Let \(A\) be the set of numbers in \(S\) divisible by 3. These are \(\{12, 15, 18, 21, 24, 27, 30\}\). The number of elements in \(A\) is \(n(A) = 7\). Let…
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