Question

Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is

• A. $\frac{1}{18}$
• B. $\frac{1}{12}$
• C. $\frac{1}{9}$
• D. none of these

Answer 1

The correct option is C

$\frac{1}{9}$

When two dice are thrown, there are $(6\times 6)=36$ outcomes

The set of all these outcomes is the sample space given by

S = (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

i.e., n(S) = 36

Let E be the event of getting a total score of 5

Then E = \{(1, 4), (2, 3), (3, 2), (4, 1)\}

$\therefore n\left(E\right)=4$

Hence, required probability $=\frac{n\left(E\right)}{n\left(S\right)}$

$=\frac{4}{36}=\frac{1}{9}$