Introduction to Probability Are the following probability as

Introduction to Probability

Are the following probability assignments valid? Explain the answer

1) Sample space= {A,B,C} and P(A)= 0.2, P(B)=0.2, P(C)=0.6

2) S= {a,b,c,d} is a sample space with P(a)=0.2, P(b)=0.2, and P(c)=0.5

a) What is the P(d) ?

b) What is the P ( {b,c}) ?

Solution

1) Sample space= {A,B,C} and P(A)= 0.2, P(B)=0.2, P(C)=0.6

Answer- These probability assignments are valid

Reason - a) prob. of each event is less than 1 and greater then 0

              b) Sum of all the probabilites ie equal to 1

                  P(A) + P(B) + P(C) = 0.2+0.2+0.6 = 1

2) S= {a,b,c,d} is a sample space with P(a)=0.2, P(b)=0.2, and P(c)=0.5

a) P(d) = 1-(P(a) + P(b) +P(c) )

          = 1-(0.2+0.2+0.5)

         = 1-0.9

         = 0.1

b) P ( {b,c}) = P(c) *P(b)

We assume that these probailities are independent to each other

P ( {b,c}) = 0.5*0.2 = 0.1

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