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

Question

A subset from the set of 9 smallest natural numbers is chosen randomly. The probability that the chosen subset contains the number 5 , is (A) (1/19) (B) (1/2) (C) (1/9) (D) (1/32)

Tardigrade Admin · Accepted Answer

n ( S )= 9 C 0+ 9 C 1+ 9 C 2+ ldots . .+ 9 C 9=29 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 ∴ P ( A )=(1/2)

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

$\frac{1}{19}$

$\frac{1}{2}$

$\frac{1}{9}$

$\frac{1}{32}$

$n (S) =^{9} C_{0} +^{9} C_{1} +^{9} C_{2} + \dots .. +^{9} C_{9} = 2^{9}$
$S = {1, 2, 3, 4, 5, 6, 7, 8, 9}$
$N (A) = (5 is one of the elements) =^{8} C_{0} +^{8} C_{1} +^{8} C_{2} + \dots\dots . +^{8} C_{0}$
$∴ P (A) = \frac{1}{2}$

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

191​

21​

91​

321​

n(S)=9C0​+9C1​+9C2​+…..+9C9​=29 S={1,2,3,4,5,6,7,8,9} N(A)=(5 is one of the elements )=8C0​+8C1​+8C2​+…….+8C0​ ∴P(A)=21​

$\frac{1}{19}$

$\frac{1}{2}$

$\frac{1}{9}$

$\frac{1}{32}$

$n (S) =^{9} C_{0} +^{9} C_{1} +^{9} C_{2} + \dots .. +^{9} C_{9} = 2^{9}$
$S = {1, 2, 3, 4, 5, 6, 7, 8, 9}$
$N (A) = (5 is one of the elements) =^{8} C_{0} +^{8} C_{1} +^{8} C_{2} + \dots\dots . +^{8} C_{0}$
$∴ P (A) = \frac{1}{2}$