Question

A loaded dice has following probability distribution of occurrences

Dice Value	1	2	3	4	5	6
Probability	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{4}$

If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is

• A. Same as that of occurrence of 3, 4, 5
• B. Same as that of occurrence of 1, 2, 5
• C. 1/128
• D. 5/8

Answer 1

The correct option is C 1/128

Probability of occurrence of 1, 5 and 6

$P(1,5,6)=\frac{1}{4}\times \frac{1}{8}\times \frac{1}{4}=\frac{1}{128}$
$[\because Dicesareindependent]$

Probability of occurrence of 3, 4, and 5

$P(3,4,5)=\frac{1}{8}\times \frac{1}{8}\times \frac{1}{8}=\frac{1}{512}$

Probability of occurrence of 1, 2 and 5

$P(1,2,5)=\frac{1}{4}\times \frac{1}{8}\times \frac{1}{8}=\frac{1}{256}$