Question

Two students from FRST 231 have the following probabilities of passing this midterm:
Probability of Student #1 passing = 0.8
Probability of Student #2 passing = 0.7
Probability of Student #1 passing given that Student #2 has passed = 0.9
a) What is the probability of both students passing?
b) What is the probability that at least one student passes?
c) Show whether or not these two events are independent.
d) What is the probability that the two students studied together?

Answer 1

P(1)=0.8

P(2)=0.7

A)

P(1|2)=0.9

P(1 and 2)/P(2) =0.9

P(1 and 2) =0.9×0.7

P(1 and 2)=0.63

Probabality of both student passing =63℅

B)

P(1 or 2) =P(1)+P(2)-P(1 and 2)

=0.8+0.7-0.63

=0.87

Probabality that at least one student passes =87%

C)

For independent events,P(1 and 2) should equal to P(1)*P(2)

Here, P(1 and 2)=0.63

P(1)*P(2)=0.8*0.7 =0.56

So,P(1 and 2) not equal to P(1)*P(2)

Thus,these two events are not independent events

D) Probabality that the two students studied together

=P(1)P(2)

=0.8*0.7

=0.56 or 56℅