Let S s1 s2 s3 s4 s5 s6 be the sample space associated with

Let S = {s₁, s₂, s₃, s₄, s₅, s₆} be the sample space associated with an experiment having the following partial probability distribution.

Consider the events:
A = {s₁, s₂, s₅}
B = {s₃, s₅, s₆}
C = {s₁, s₃, s₄, s₆}
D = {s₁, s₂, s₃}

Calculate the following probabilities. (Enter your answers as fractions.)

(a) P(s₂)=   

(b) P(D)=  

(c) P(B^C)=  

(d) P(A^C B) =  

(e) P(C^C D) =  

Solution

The probabilities of S should add up to 1.

Thus,

a)

P(s2) = 1 - 2/19 - 4/19 - 4/19 - 2/19 - 1/19 = 6/19 [answer]

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b)

P(D) = P(s1) + P(s2) + P(s3) = 12/19 [answer]

**********

c)

P(Bc) = 1 - P(B) = 1 - [P(s3) + P(s5) + P(s6)] = 12/19 [answer]

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d)

P(Ac n B) = P(s3) + P(s6) = 5/19 [answer]

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e)

P(Cc U D) = P(s1) + P(s2) + P(s3) + P(s5) = 14/19 [answer]