Choose the correct answer from the given four options. Two dice a… - Vidyadip

MCQ

Choose the correct answer from the given four options. Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6,$ the probability of getting a sum $3,$ is:

A
$\frac{1}{18}$
B
$\frac{5}{18}$
✓
$\frac{1}{5}$
D
$\frac{2}{5}$

✓

Answer

Correct option: C.

$\frac{1}{5}$

Let $E_1 =$ Event that the sum of numbers on the dice was less than $6$
And $E_2=$ Event that the sum of numbers on the dice is $3.$
$\therefore E_1 = \{(1, 4), (4, 1), (2, 3), (3, 2), (2, 2), (1, 3), (3, 1), (1, 2), (2, 1), (1, 1)\}$
$\Rightarrow n(E_1) = 10$
And $E_2 = \{(1, 2), (2, 1)\}$
$\Rightarrow n(E_2) = 2$
$\therefore$ Required Probability $=\frac{2}{10}=\frac{1}{5}$

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