Question

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

$$\begin{array}{ccccccc}Outcome& 1& 2& 3& 4& 5& 6\\ Frequency& 165& 175& 180& 150& 145& 185\end{array}$$

(i) What is the probability of getting a multiple of 2
(ii) What is the probability of getting a multiple of 3
(iii) are (i) and (ii) mutually exclusive?

Answer 1

Number of times a 2 or 4 or 6 was rolled = 175 + 150 + 185 = 510
Probability of getting a multiple of 2 = 510/1000 = 0.51
Number of times a 3 or 6 was rolled = 180 + 185 = 365
Probability of getting a multiple of 2 = 365/1000 = 0.365
These two events are not mutually exclusive because they have one outcome “6” which is common to both.