Question

Tommy is a new student at FAU. He notices that some students ride skateboards around campus. He also sees that some students live in the dorms on campus. When Tommy accesses the FAU website, he sees that 20% of FAU students live in dorms. 30% of FAU students ride skateboards around campus. If a FAU student lives in a dorm, there is a 65% chance that they ride a skateboard around campus.

	Skates	Doesn’t Skate
Dorm
No Dorm

Fill out the joint probability table.

1. What is the probability that a student doesn’t live in a dorm or doesn’t skateboard?

2. If a student skateboards, what is the probability that they live in a dorm?

3. If a student doesn’t live in a dorm, what is the probability that they skateboard around campus?

4. Are living in a dorm and skateboarding independent events?

Answer 1

Ans:

P(skates/dorm)=0.65

P(skates and dorm)=P(skates/dorm)*P(dorm)=0.65*0.2=0.13

	Skates	Does not skates	Total
Dorm	0.13	0.07	0.2
No Dorm	0.17	0.63	0.8
Total	0.3	0.7	1

a)

P(does not skates or does not live in dorm)

=P(does not skates)+P(does not live in dorm)- P(does not skates and does not live in dorm)

=0.7+0.8-0.63

=0.87

b)

P(dorm/skateboard)=P(dorm and skateboard)/P(skateboard)

=0.13/0.3=0.433

c)

P(skateboard/not dorm)=P(skateboard and no dorm)/P(no dorm)=0.17/0.8=0.2125

d)

P(skateboard/dorm)=0.65

P(skateboard)=0.3

As,P(skateboard/dorm) is not equal to P(skateboard),so both events are not independent.