JEE MAIN - Mathematics (2022 - 27th June Evening Shift - No. 22)
Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that $$P({E_n}) = {n \over {36}}$$ for every n = 1, 2, ........, 8. Then the number of elements in the set $$\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}$$ is ___________.
Answer
19
Explanation
Here $$P({E_n}) = {n \over {36}}$$ for n = 1, 2, 3, ......, 8
Here $$P(A) = {{Any\,possible\,sum\,of\,(1,2,3,\,...,\,8)( = a\,say)} \over {36}}$$
$$\because$$ $${a \over {36}} \ge {4 \over 5}$$
$$\therefore$$ $$a \ge 29$$
If one of the number from {1, 2, ......, 8} is left then total $$a \ge 29$$ by 3 ways.
Similarly by leaving terms more 2 or 3 we get 16 more combinations.
$$\therefore$$ Total number of different set A possible is 16 + 3 = 19
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