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Chapter 3: 3 (page 168)

The sample space for an experiment contains five sample points with probabilities as shown in the table. Find the probability of each of the following events:

a. Either 1,2 or 3 occurs

b. Either 1,3 or 5 occurs

c. 4 does not occur

Short Answer

Expert verified

a.PA=0.55,b.PB=0.50,c.P(C)=0.70

Step by step solution

01

Finding the probability of event  A

To calculate the probability of event A happening, we add the individual probabilities of sample points 1, 2 and 3.

Given,

A: Either 1,2 or 3 occurs

P(A)=P(1)+P(2)+P(3)P(A)=0.05+0.20+0.30P(A)=0.55PA=P1+P2+P3PA=0.05+0.20+0.30PA=0.55

Hence, P(A)=0.55PA=0.55

02

Finding the probability of event  B

To calculate the probability of event B happening, we add the individual probabilities of sample points 1, 3 and 5.

B: Either 1,3 or 5 occurs

P(B)=P(1)+P(3)+P(5)P(B)=0.05+0.30+0.15P(B)=0.50PB=P1+P3+P5PB=0.05+0.30+0.15PB=0.50

Hence, P(B)=0.50PB=0.50

03

Finding the probability of event C

To calculate the probability of event C happening, we subtract the probability of sample point 4 occurring from 1.

C: 4 does not occur

P(C)=1-P(C)P(C)=1-0.30P(C)=0.70PC=1-PCPC=1-0.30PC=0.70

Hence,P(C)=0.70PC=0.70

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