A large university: 60% of students have a facebook page theyve checked today12% of students have an instagram page theyve checked todayIncluded in those percentages is the 3% whove checked today. a) is the event F (checked facebook) independent of event I (checked instagram)b) is the event F (checked facebook) mutaually exclussive of event I (checked instagram)

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Asked Sep 4, 2019
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A large university:

 

60% of students have a facebook page theyve checked today

12% of students have an instagram page theyve checked today

Included in those percentages is the 3% whove checked today.

 

a) is the event F (checked facebook) independent of event I (checked instagram)

b) is the event F (checked facebook) mutaually exclussive of event I (checked instagram)

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Expert Answer

Step 1

a) Independence of events:

If probability of happening of one event does not affect the probability of happening of another event, then the two events are said to be independent. The multiplication rule to check the independence of two events F and I is given below.

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P(FI)P(F)x P(I)

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Step 2

Is the events F and I are independent?

It is given that 3% of the student checked both Instagram and Facebook.

P(F I) = P(a randomly selected student checked Instagram and Facebook)

That is, P(F I) = 0.03.

           P(F) × P(I) = 0.6 × 0.12

                                 = 0.072

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