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QJEEM22Ma2cc9: JEE Main 2022 Mathematics - Class 12 JEEM22Ma2cc9 Solution: Let S = {E 1 , E 2 , ........., E 8 } be a sample space of a…

Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that P(En)=n36P({E_n}) = {n \over {36}} for every n = 1, 2, ........, 8. Then the number of elements in the set {A⊆S:P(A)≥45}\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\} is ___________.

Step-by-Step Verified Solution

Here P(En)=n36P({E_n}) = {n \over {36}} for n = 1, 2, 3, ......, 8

Here P(A)=Any possible sum of (1,2,3, ..., 8)(=a say)36P(A) = {{Any\,possible\,sum\,of\,(1,2,3,\,...,\,8)( = a\,say)} \over {36}}

∵\because a36≥45{a \over {36}} \ge {4 \over 5}

∴\therefore a≥29a \ge 29

If one of the number from {1, 2, ......, 8} is left then total a≥29a \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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