Q. Two numbers are selected randomly from the set $S = \{ 1,\ 2,\ 3,\ 4,\ 5,\ 6\}$ without replacement one by one. The probability that minimum of the two numbers is less than, 4 is

A) 1/15
B) 14/15
C) 1/5
D) 4/5
Explanation

(d)
Here, two numbers are selected from {1,2,3,4,5,6,}
$\Rightarrow n(S) = 6 \times 5\${as one by one without replacement}
Favourable cases,
[table] First number | Possible value for second number ; 1 | 2, 3, 4, 5, 6 ; 2 | 3, 4, 5, 6 ; 3 | 4, 5, 6 [/table]
There are 12 ways but the numbers may be interchanged
$\therefore\ n(E) = 2 \times 12 = 24$
$\therefore$ Required probability$= \frac{n(E)}{n(S)} = \frac{24}{30} = \frac{4}{5}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.