3. Let A, B, C be three events such that P(A) = 0:5, P(B) = 0:6, P(C) = 0:8(a) Can any two of these events be mutually exclusive? Explain your conclusion. (b) Assuming that theevents are independent, compute P(ASBSC).4. Let A and B be events such that P(A) = 0:7 and P(B) = 0:8.(a) Circle the possible values of P(ATB): 0:3 0:5 0:8 0:9(b) Circle the possible values of P(ASB): 07 0:8 1You need to explain each of your conclusions. For example, if you think that P(ATB) can be 0:5, youdraw the corresponding Venn diagram, and if you think that P(ASB) cannot be 1, you support your claimwith suitable formulas.5. A student is applying to MBA programs at Harvard, Yale, and MIT. Accordingly, the student preparesthree personalized application letters and three addressed envelopes. Unfortunately, after three nights of heavystudying, the student is somewhat disoriented and places the letters in the envelopes at random. What is theprobability that at least one letter ended up in the correct envelope?
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