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(A) A coin is dropped at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with radius $0.7\text{ m}$?
OR
(B) A die is thrown twice. What is the probability that (i) difference between two numbers obtained is 3? (ii) sum of the numbers obtained is 8?
OR
(B) A die is thrown twice. What is the probability that (i) difference between two numbers obtained is 3? (ii) sum of the numbers obtained is 8?
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(A) Area of circle $= \frac{22}{7} \times \frac{7}{10} \times \frac{7}{10} = \frac{154}{100}\text{ sq m}$ [$\frac{1}{2}$ mark]
Area of rectangle $= 6\text{ sq m}$ [$\frac{1}{2}$ mark]
$P(\text{coin lands inside the circle}) = \frac{154/100}{6} = \frac{154}{600}$ or $\frac{77}{300}$ [$1$ mark]
OR
(B) (i) $P(\text{difference between two numbers obtained is 3}) = \frac{6}{36}$ or $\frac{1}{6}$ [$1$ mark]
(ii) $P(\text{sum of numbers obtained is 8}) = \frac{5}{36}$ [$1$ mark]
Area of rectangle $= 6\text{ sq m}$ [$\frac{1}{2}$ mark]
$P(\text{coin lands inside the circle}) = \frac{154/100}{6} = \frac{154}{600}$ or $\frac{77}{300}$ [$1$ mark]
OR
(B) (i) $P(\text{difference between two numbers obtained is 3}) = \frac{6}{36}$ or $\frac{1}{6}$ [$1$ mark]
(ii) $P(\text{sum of numbers obtained is 8}) = \frac{5}{36}$ [$1$ mark]