Three identical dice are rolled. The probability that same number will appear on each of them will be:

Question

Three identical dice are rolled. The probability that same number will appear on each of them will be: (A)  (1/6)  (B)  (1/36)  (C)  (1/18)  (D)  (3/28)

Tardigrade Admin · Accepted Answer

Total number of cases, n(S)=63 Total number of favourable cases, in which all three dice have Same number, n(F)=6 ∴ Required probability =(6/63) =(1/36)

Q. Three identical dice are rolled. The probability that same number will appear on each of them will be:

$\frac{1}{6}$

$\frac{1}{36}$

$\frac{1}{18}$

$\frac{3}{28}$

Total number of cases, $n (S) = 6^{3}$
Total number of favourable cases,
in which all three dice have Same number, $n (F) = 6$
$∴$ Required probability $= \frac{6}{6 ^{3}}$
$= \frac{1}{36}$

Q. Three identical dice are rolled. The probability that same number will appear on each of them will be:

61​

361​

181​

283​

Total number of cases, n(S)=63 Total number of favourable cases, in which all three dice have Same number, n(F)=6 ∴ Required probability =636​ =361​

$\frac{1}{6}$

$\frac{1}{36}$

$\frac{1}{18}$

$\frac{3}{28}$

Total number of cases, $n (S) = 6^{3}$
Total number of favourable cases,
in which all three dice have Same number, $n (F) = 6$
$∴$ Required probability $= \frac{6}{6 ^{3}}$
$= \frac{1}{36}$