Three numbers are chosen at random without replacement from : 1,2… - Vidyadip

MCQ

Three numbers are chosen at random without replacement from :$\{1,2,3,4,5,6,7,8\}$. The probability that their minimum is $3,$ given that their maximum is $6$, is :

✓
$\frac{1}{5}$
B
$\frac{1}{4}$
C
$\frac{2}{5}$
D
$\frac{3}{8}$

✓

Answer

Correct option: A.

$\frac{1}{5}$

a
$3$ numbers are chosen from $\{1,2,3, \ldots ., 8\}$ without replacement. Let $A$ be the event that the maximum of chosen numbers is $6$. Let $\mathrm{B}$ be the event that the minimum of chosen numbers is $3 .$

$P(B/A) = \frac{{P(A \cap B)}}{{P(B)}}$

$ = \frac{{\frac{{1 \cdot 1 \cdot 2}}{{{\,^8}{C_3}}}}}{{\frac{{^5{C_2}}}{{^8{C_3}}}}} = \frac{2}{{10}} = \frac{1}{5}$

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