Question

The outcomes of 65 throws of a dice were noted as shown below:

Outcome	1	2	3	4	5	6
Number of times	8	10	12	16	9	10

A dice is thrown at random. What is the probability of getting a prime number?
(a) $\frac{3}{35}$

(b) $\frac{3}{5}$

(c) $\frac{31}{65}$

(d) $\frac{36}{65}$

Answer 1

(c) $\frac{31}{65}$

Explanation:
Total number of throws = 65
Let E be the event of getting a prime number.
Then, E contains 2, 3 and 5, i.e. three numbers.

∴ P(getting a prime number) = P(E) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{times}\mathrm{prime}\mathrm{number}\text{s}\mathrm{occur}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{throws}}=\frac{(10+12+9)}{65}=\frac{31}{65}$