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Chapter 3: Q30E (page 180)

Suppose P(A)=.4,P(B)=.7,andP(A鈭�B)=.3.

Find the following probabilities:

  1. P(BC)
  2. P(AC)
  3. P(A鈭�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鈭�P(B)=1鈭�0.7=0.3

Hence, P(Bc) is0.3.

02

Find the probabilities

P(Ac)=1鈭�P(A)=1鈭�0.4=0.6

Hence, P(Ac) is0.6.

03

Find the probabilities

P(A鈭�B)=P(A)+P(B)鈥�鈭�P(A鈭�B)=0.4+0.7鈭�0.3=0.8

Hence,P(A鈭�B)is0.8.

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Consider the Venn diagram in the next column, where

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

Find each of the following probabilities:

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

Compute the number of ways can select n element from N element of each of the following:

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See all solutions

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