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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:

Outcome123456Frequency165175180150145185

(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?

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Solution

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.


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