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

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 $16+3=19$