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Chapter 3: Q30E (page 180)

Suppose P(A)=.4,P(B)=.7,andP(A∩B)=.3.

Find the following probabilities:

  1. P(BC)
  2. P(AC)
  3. P(A∩B)

Short Answer

Expert verified
  1. 0.3
  2. 0.6
  3. 0.8

Step by step solution

01

Find the probabilities

The complement of an event A is the event that does not occur; that is, the event composed of all sample points not included in event A. denotes the complement of A.

P(Bc)=1−P(B)=1−0.7=0.3

Hence, P(Bc) is0.3.

02

Find the probabilities

P(Ac)=1−P(A)=1−0.4=0.6

Hence, P(Ac) is0.6.

03

Find the probabilities

P(A∪B)=P(A)+P(B)​−P(A∩B)=0.4+0.7−0.3=0.8

Hence,P(A∪B)is0.8.

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Most popular questions from this chapter

In a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. One of the 106 social robots is randomly selected and the design (e.g., wheels only) is noted.

  1. List the sample points for this study.
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  3. What is the probability that the selected robot is designed with wheels?
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P(E1)=0.10,P(E2)=0.05,P(E3)=P(E4)=0.2,P(E5)=0.6,P(E6)=0.3,P(E7)=0.06andP(E8)=0.3

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a.P(Ac)b.P(Bc)c.P(Ac∩B)d.P(A∪B)e.P(A∩B)f.P(Ac∩Bc)

g. Are events A and B mutually exclusive? Why?

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