# Ex.15.2 Q2 Probability Solution - NCERT Maths Class 10

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## Question

A die is numbered in such a way that its faces show the numbers $$1, 2, 2, 3, 3, 6$$. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws: What is the probability that the total score is (i) even? (ii) $$6$$? (iii) at least $$6$$?

## Text Solution

What is known?

A die is numbered in such a way that its faces show the numbers $$1, 2, 2, 3, 3, 6$$. It is thrown two times and the total score in two throws is noted

What is  unknown?

What is the probability that the total score is (i) even? (ii) $$6$$? (iii) at least $$6$$?

Reasoning:

To solve this question, first find out the total number of outcomes and all the possible outcomes. Now, to find the probability use the formula given below

\begin{align}\text{Probability}=\frac{\text{ No of possible outcomes }}{\text{ no of outcomes }}\end{align}

Step:

 + 1 2 2 3 3 6 1 2 3 3 4 4 7 2 3 4 4 5 5 8 2 3 4 4 5 5 8 3 4 5 5 6 6 9 3 4 5 5 6 6 9 6 7 8 8 9 9 12

Total number of possible outcomes $$= 6 \times 6 =36$$

(i) No of possible outcomes when the sum is even $$= 18$$

Probability that the total score is even
\begin{align} & =\frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes }} \\& =\frac{18}{36}\\&=\frac{1}{2} \\\end{align}

(ii) No of possible outcomes when the sum is $$6 = 4$$

Probability that of getting the sum $$6$$
\begin{align} & =\frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes }} \\& =\frac{4}{36}\\&=\frac{1}{9}\end{align}

(iii) No of possible outcomes when the sum is at-least6(greater than $$5$$) $$= 15$$

Probability that of getting the sum at-least $$6$$
\begin{align} & =\frac{\text{No of possible outcomes }}{\text{Total no of outcomes}} \\& =\frac{15}{36}\\&=\frac{5}{12}\end{align}

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