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

Question

Answer 1

Concept:

P(A/B) = $\frac{P (A \cap B)}{P (B)} = \frac{n (A \cap B)}{n (B)}$

Calculation:

Given two dice are thrown.

⇒ n(S) = 36

Let E1 be the event sum of numbers on the dice was less than 6,

∴ E1 = {(1,4), (4,1), (2,3), (3,2), (2,2), (1,3), (3,1), (1,2), (2,1) ,(1,1)}

⇒ n(E₁) = 10

Let E₂ be the event sum of numbers on the dice 3,

∴ E1= {(1,2), (2,1)}

⇒ n(E₂) = 2

E₁∩ E₂ = {(1,2), (2,1)}

n(E1∩ E2) = 2

We need to find P(E₂| E₁)=

\frac{P (E_{2} \cap E_{1})}{P (E_{1})} = \frac{n (E_{2} \cap E_{1})}{n (E_{1})}

=

\frac{2}{10}

=

\frac{1}{5}

∴ The required probability is 1/5.

The correct answer is option 3.

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