Suppose that the probability that Michael Jordan Will fail a certain statistics

Question

Suppose that the probability that Michael Jordan Will fail a certain statistics examination is 0.7, the probability that Joe Montana will fail the examination is 0.4, and the probability that both students will fail the examination is 0.3.

a) What is the probability that at least one of these students will fail the examination?

b) What is the probability that Michael Jordan will fail the examination, but Joe montana will pass the examination?

c) If at least one of these two students failed the examination, what is the probability that Micahel Jordan will fail the examination?

d) Is the event that Micahel Jordan fails the examination independent of the event that Joe Montana fails the examination? Justify mathematically!

Explanation / Answer

A. P(e)=0.7*0.6+0.3*0.6+0.3=0.42+0.18+0.3=0.9

B.0.7*0.6=0.42

C.0.7*0.6+0.3=0.72

D. P(And B)=P(A).P(b) if A and B are independent but o.7*0.4=0.28 and not equal to 0.3 hence not independent

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