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lara31 [8.8K]
3 years ago
8

A die is rolled. What is the probability that the number is a factor of 6 or more than 2? Does this scenario represent mutually

exclusive or mutually inclusive events?
Mathematics
1 answer:
goblinko [34]3 years ago
6 0

Factors of 6 are : 1,2,3 and 6.

Let us find probability of getting the number that is a factor of 6.

P(\text{ The number is a factor of 6})=\frac{4}{6} =\frac{2}{3}

Now let us find probability of getting a number more than 2 (3,4,5,6).

P(\text{ The number is a greater than 2})=\frac{4}{6} =\frac{2}{3}

We can see that these two events are mutually inclusive events. We can find probability of mutually inclusive events by formula P(\text{X or Y})=P(X)+P(Y)-P(\text{X and Y}).  

P(\text{ The number is a factor of 6 and greater than 2})=\frac{2}{6} =\frac{1}{3}

Now we will find probability of getting the number is a factor of 6 or more than 2 using above formula.

P(\text{ The number is a factor of 6 or greater than 2})=\frac{2}{3} +\frac{2}{3}-\frac{1}{3}    

P(\text{ The number is a factor of 6 or greater than 2})= \frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1  

Therefore, our probability will be 1 and this scenario represents mutually inclusive events.  

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