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) what is the probability that a randomly selected student checked facebook or instagram?b) what is the probability that someone checked instagram GIVEN that they've checked facebookc) what is the probability someone has checked neither instagram nor facebook?d) is the event F (checked facebook) independent of event I (checked instagram)e) is the event F (checked facebook) mutaually exclussive of event I (checked instagram)

Question
Asked Sep 3, 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) what is the probability that a randomly selected student checked facebook or instagram?

b) what is the probability that someone checked instagram GIVEN that they've checked facebook

c) what is the probability someone has checked neither instagram nor facebook?

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

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

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Expert Answer

Step 1

Note:

Hi! Thank you for posting the question. However, your question has more than 3 parts. So, according to our policy, we have solved the first 3 parts for you.

Please note that, it is said, “Included in those percentages is the 3% whove checked today.” This does not make sense. Logically, it should have bee “Included in those percentages is the 3% who’ve checked both today.” We have solved the problems, assuming this factor.

Step 2

Part (a):

For 2 events A, B with an intersection region between them, P (A ∪ B) = P (A) + P (B) – P (A ∩ B). Thus,

P (a randomly selected student checked Facebook or Instagram)

= P (a randomly selected student checked Facebook union a randomly selected student checked Instagram)

= P (a randomly selected student checked Facebook) + P (a randomly selected student checked Instagram) – P (a randomly selected student checked both)

= 0.60 + 0.12 – 0.03

= 0.69.

Thus, the probability that a randomly selected student checked Facebook or Instagram is 0.69.

Step 3

Part (b):

For an event A, given that B has already occurred, the probability of A given B, that is, P (A | B) = P (A ∩ B) / P (B). Thus,

P (someone checked Instagram GIVEN that they've checked Facebook)

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

= P (a randomly sele...

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