Question

4.40 An experiment can result in one of five equally likely simple events, El, E2.. . . , E, Events A, B, and C are defined as follows: A: E, E P(A)-4 C: Es, E P(C)-4 Find the probabilities associated with the following events by listing the simple events in each

Find P(A and B)

E1 is in both of them.

Answer 1

ANSWER:

An experiment can result in one of five equally likely simple events, E₁, E₂, . . . , E⁵. Events A, B, and C are defined as follows:

A: E1, E3 B. El. E2. E4, Es C: E3, E4 4 P(A) = .4 P(B) = .8 P(C) = .4 0

Find the probabilities associated with the following events by listing the simple events in each.

a. Ac e. BC h.(ANB) f. AB g.AUBUC

We have,

​​​​​​​

2 48) ABA

1. Consider,

   The event

   

   = .2

   (From Conditional probability)

   P(AnB)

   

   

   = 0.25

   (b)

2. Consider,

   The event

   

   5 P(BnC)

   = .2

   (From Conditional probability)

   P(B|C) P(BIC)- P(C)

   =

   4

   = .5

(a)

Consider,

P(A)P(B)

= (A)(A)

And

P(AnB) 25

Events A and B are not independent, since these probabilities are not the same.

(b)

= .25

0

Events A and B are not mutually exclusive, since the probability is not equal to zero.

(a) (Addition rule)

P(AUB)-P(A)+P(B)-P(AnB)

1. (Multiplication rule)

   

   4 +8-(.8 (.25)

   

2. (b) (Multiplication rule)

   

   = (.25)(8)

   

   = 0.2

3. (Multiplication rule)

4. 

   = (5)(4)

   

   = 0.2

   Yes, I agree, because both the results are same.

a) P(A|B) = P(A and B)/P(B) = 0.2/0.8 = 0.25

b) P(B | C) = P(B and C)/P(C) = 0.2/0.4 = 0.5