Question:
The probability of throwing a number greater than 2 with a fair die is
(a) $\frac{2}{5}$
(b) $\frac{5}{6}$
(C) $\frac{1}{3}$
(d) $\frac{2}{3}$
Solution:
Total number of outcomes = 6.
Out of the given numbers, numbers greater than 2 are 3, 4, 5 and 6.
Numbers of favourable outcomes = 4.
$\therefore \mathrm{P}($ getting a number greater than 2$)=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$
$=\frac{4}{6}=\frac{2}{3}$
Thus, the probability of getting a number greater than 2 is $\frac{2}{3}$.
Hence, the correct answer is option (d).