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Mathematics · Probability · NCERT Examples

Example 13

A complete, independently verified solution for NCERT Example 13.

Mathematics · Chapter 14 · NCERT Examples

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NCERT Example

Example 13

two dice · sample space · sum

A blue die and a grey die are thrown together. Write all possible outcomes and find the probability that the sum of the top numbers is (i) 8, (ii) 13 and (iii) less than or equal to 12.

Six by six outcome table for a blue die and a grey die, with the five ordered pairs whose sum is 8 outlined.
Figure 14-3 from the supplied NCERT chapter.

Solution

Board-exam working:

The ordered pair records (blue die, grey die). The 6 × 6 table gives 36 equally likely outcomes.

n(S)=6×6=36n(S)=6\times6=36

(i) Outcomes whose sum is 8:

E={(2,6),(3,5),(4,4),(5,3),(6,2)}E=\{(2,6),(3,5),(4,4),(5,3),(6,2)\}
P(E)=536P(E)=\frac5{36}

(ii) The largest possible sum is 12, so a sum of 13 is impossible.

P(sum 13)=036=0P(\text{sum }13)=\frac0{36}=0

(iii) Every outcome has sum at most 12.

P(sum≤12)=3636=1P(\text{sum}\le12)=\frac{36}{36}=1

Final answer

(i) 536(ii) 0(iii) 1\boxed{\text{(i) }\frac5{36}\qquad\text{(ii) }0\qquad\text{(iii) }1}