Question

A dice is thrown 300 times and the outcomes are noted as given below.

Outcome	1	2	3	4	5	6
Frequency	60	72	54	42	39	33

When a dice is thrown at random, what is the probability of getting a
(i) 3?
(ii) 6?
(iii) 5?
(iv) 1?

Answer 1

Total number of throws = 300
In a random throw of a dice, let E₁, E₂, E₃, E₄, be the events of getting 3, 6, 5 and 1, respectively. Then,
(i) P(getting 3) = P(E₁) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{times}3\mathrm{appears}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{tr}\text{ia}\mathrm{ls}}=\frac{54}{300}=0.18$

(ii) P(getting 6) = P(E₂) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{times}6\mathrm{appears}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{tr}\text{ia}\mathrm{ls}}=\frac{33}{300}=0.11$

(iii) P(getting 5) = P(E₃) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{times}5\mathrm{appears}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{tr}\text{ia}\mathrm{ls}}=\frac{39}{300}=0.13$

(iv) P(getting 1) = P(E₄) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{times}1\mathrm{appears}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{tr}\text{ia}\mathrm{ls}}=\frac{60}{300}=0.20$