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

Question

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) (1/18) (B) (5/18) (C) (1/5) (D) (2/5)

Tardigrade Admin · Accepted Answer

When two dice are thrown, then the number of events in the sample space

= 36

Let

A

: sum of the numbers on the dice was less than 6 and

B

: getting a sum equals to 3 .
Then,

A = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3) . (3, 1), (3, 2), (4, 1)}

B = {(1, 2), (2, 1)}

and

A \cap B = {(1, 2), (2, 1)}

∴ P (A \cap B) = \frac{2}{36} = \frac{1}{18}

P (A) = \frac{10}{36} = \frac{5}{18}

Now,

P (\frac{B}{A}) = \frac{P ( A \cap B )}{P ( A )} = \frac{\frac{1}{18}}{\frac{5}{18}} = \frac{1}{5}

Q. 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

$\frac{1}{18}$

$\frac{5}{18}$

$\frac{1}{5}$

$\frac{2}{5}$

Q. 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

181​

185​

51​

52​

$\frac{1}{18}$

$\frac{5}{18}$

$\frac{1}{5}$

$\frac{2}{5}$