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Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Current Population Survey, P(A)=0.138, P(B)=0.261, and the probability that a household is both prosperous and educated is P(A and B)=0.082. What is the probability P(A or B) that the household selected is either prosperous or educated?

Respuesta :

JeanaShupp

Answer:  0.317

Step-by-step explanation:

Let A be the event that the selected household is prosperous and B the event that it is educated.

Given : P(A)=0.138,   P(B)=0.261

P(A and B)=0.082

We know that for any events M and N ,

[tex]\text{P(M or N)=P(M)+P(N)-P(M or N)}[/tex]

Thus , [tex]\text{P(A or B)=P(A)+P(B)-P(A or B)}[/tex]

[tex]\text{P(A or B)}=0.138+0.261-0.082\\\\\Rightarrow\text{ P(A or B)}=0.317[/tex]

Hence, the probability P(A or B) that the household selected is either prosperous or educated = 0.317

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