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Chapter 3: Q81E (page 200)

Suppose the events B1and B2are mutually exclusive and complementary events, such thatP(B1)=.75andP(B2)=.25 Consider another event A such that role="math" localid="1658212959871" P(AB1)=.3, role="math" localid="1658213029408" P(AB2)=.5.

  1. FindP(B1鈭�A).
  2. FindP(B2鈭�A)
  3. Find P(A) using part a and b.
  4. Findrole="math" localid="1658213127512" P(B1A).
  5. Findrole="math" localid="1658213164846" P(B2A).

Short Answer

Expert verified

The values of probabilities in all parts are:

  1. 0.225
  2. 0.125
  3. 0.35
  4. 0.64
  5. 0.357

Step by step solution

01

Important formula

The general rule of multiplication is P(A鈭�B)=P(A)脳P(BA).

02

Find P(B1∩A).

P(B1鈭�A)=P(AB1).P(B1)=(0.3)(0.75)=0.225

So, the values of probabilities in all parts are 0.225

03

Find P(B2∩A)

P(B2鈭�A)=P(AB2).P(B2)=(0.25)(0.5)=0.125

Hence, the values of probabilities in all parts are 0.125

04

Find P(A)

P(A)=P(B1鈭�A)+P(B2鈭�A)=0.225+0.125=0.35

Accordingly, the values of probabilities in all parts are 0.35

05

Find P(B1A)

P(B1A)=P(B1鈭�A)P(A)=0.2250.35=0.64

Henceforth, the values of probabilities in all parts are 0.64

06

Find P(B2A)

P(B2A)=P(B2鈭�A)P(A)=0.1250.35=0.357

Therefore, the values of probabilities in all parts are 0.357

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