Question

Let S = {E₁, E₂, ……………., E₈} be a sample space of a random experiment such that \(P(E_n) = \frac{n}{36}\) for every n = 1, 2, ………, 8. Then the number of elements in the set\(\{ A \subseteq S : P(A) \geq \frac{4}{5} \}\) is_________.

Answer 1

Correct Answer: 19

Here \(P(E_n) = \frac{n}{36}\) for n = 1, 2, 3, ………, 8
Here,
\(P(A) = \frac{\text{Any possible sum of }(1,2,3,\ldots,8) \, (= a \, \text{say})}{36}\)
\(∵ \frac{a}{36}≥\frac{4}{5}\)
\(∴ a ≥ 29\)
If one of the number from {1, 2, …., 8} is left then total \(a ≥ 29\) by 3 ways.
Similarly by leaving terms more 2 or 3 we get 16 more combinations.
∴ Total number of different set A possible is \(16+3=19\)