Question

The probability of getting a total of 10 in a single throw of the dice is

• A. $\frac{1}{9}$
• B. $\frac{1}{12}$
• C. $\frac{1}{6}$
• D. $\frac{5}{36}$

Answer 1

The correct option is B

$\frac{1}{12}$

When two dices 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 10

Then E = \{(4, 6), (5, 5), (6, 4)\}

$\therefore n\left(E\right)=3$

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

$=\frac{3}{36}=\frac{1}{12}$