Question

If the probability that a family will buy a vacation home in Manmi, Malibu, or Newport is 0.25, 0.10, 0.35, what is the probability the family will consummate one of these transactions? please show all wor with explanation.

Answer 1

consummate one of these transactions means for this we get three condtion

1 ] ( Miamia and Not In Malibu and Not In NewPort )

2 ] ( Not In Miamia and Malibu and Not In NewPort )

3] ( Not In Miamia and Not In Malibu and NewPort )

We use complete rule

P ( A' ) = 1 - P ( A )                                A' : means the complement of A

We have Given P(Miami)=0.25 Thereore we get P(Not In Miami)=1-0.25=0.75

P(Malibu)=0.1 Thereore we get P(Not In Malibu)=0.9

P(Newport)=0.35 Thereore we get P( Not In Newport)=0.65

P( family will consummate one of these transactions )=P(Miami)* P(Not In Malibu)*P( Not In Newport)

+     P(Not In Miami)* P(Malibu)*P( Not In Newport) + P(not In Miami)*P(not In Malibu)*P( Newport)

=0.25*0.9*0.65 + 0.75* 0.1 * 0.65 + 0.75*0.9*0.35 = 0.43125

Final answer : -

Probability that family will consummate one of these transactions = 0.43125