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The sample space of a random experiment is {a,b,c,d,e} with probabilities 0.1,0.1,0.2,0.4, and 0.2, respectively. Let A denote the event {a,b,c}, and let B denote the even t {c,d,e}. Determine the following:

a. P(A)
b. P(B)
c. P(A’)
d. P(AUB)
e. P(AnB)

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Answer with Step-by-step explanation:

We are given that a sample space

S={a,b,c,d,e}

P(a)=0.1

P(b)=0.1

P(c)=0.2

P(d)=0.4

P(e)=0.2

a.A={a,b,c}

P(A)=P(a)+P(b)+P(c)

P(A)=0.1+0.1+0.2=0.4

b.B={c,d,e}

P(B)=P(c)+P(d)+P(e)=0.2+0.4+0.2=0.8

c.A'=Sample space-A={a,b,c,d,e}-{a,b,c}={d,e}

P(A')=P(d)+P(e)=0.4+0.2=0.6

d.[tex]A\cup B[/tex]={a,b,c,d,e}

[tex]P(A\cup B)[/tex]=P(a)+P(b)+P(c)+P(d)+P(e)=0.1+0.1+0.2+0.4+0.2=1

e.[tex]A\cap B[/tex]={c}

[tex]P(A\cap B)=P(c)=0.2[/tex]

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