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  4. A subset from the set of 9 smallest natural numbers is chosen randomly. The probability that the chosen subset contains the number 5 , is

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Q. A subset from the set of 9 smallest natural numbers is chosen randomly. The probability that the chosen subset contains the number 5 , is

Probability - Part 2

Solution:

$ n ( S )={ }^9 C _0+{ }^9 C _1+{ }^9 C _2+\ldots . .+{ }^9 C _9=2^9 $
$S =\{1,2,3,4,5,6,7,8,9\} $
$N ( A )=(5 \text { is one of the elements })={ }^8 C _0+{ }^8 C _1+{ }^8 C _2+\ldots \ldots .+{ }^8 C _0$
$\therefore P ( A )=\frac{1}{2}$