Question

An unbiased cubic die marked with $1,2,2,3,3,3$ is rolled 3 times. The probability of getting a total score of 4 or 6 is

• A. $\frac{16}{216}$
• B. $\frac{50}{216}$
• C. $\frac{60}{216}$
• D. none

Answer 1

Answer: (B)

$1,2,2,3,3,3$ (thrown 3 times)
$P(1)=\frac{1}{6};P(2)=\frac{2}{6};P(3)=\frac{3}{6}$
$P(S)=P(4\text{ or }6)=P(112(3\text{ cases })\text{ or }123(6\text{ cases })\text{ or }222)$
$=3\cdot \frac{1}{6}\cdot \frac{1}{6}\cdot \frac{2}{6}+6\frac{1}{6}\cdot \frac{2}{6}\cdot \frac{3}{6}+\frac{2}{6}\cdot \frac{2}{6}\cdot \frac{2}{6}=\frac{6+36+8}{216}=\frac{50}{216}=\frac{25}{108}$