Question

Question 3. Sarah finds that condos account for 35% of residential properties in Austin, and the rest 65% are houses. 1. She randomly selects 5 residential properties in this neighborhood. What is the probability that 2 out of these properties are condos? (2 Points) 2. Mr. Hayes, Sarah’s father, randomly selects 30 residential properties in Austin. What is the probability that fewer than 10 out of these properties are condos?(4 Points) 3. Sarah would like to have a garden in their new home. In the neighborhood of interest, only 10% of condos currently have a garden, another 8% of condos have the capacity of accommodating a garden, yet have not had a garden installed. If she randomly selects a PROPERTY in Austin, what is the probability that the property is a condo WITHOUT a capacity of having a garden?(2 Points) 4. In the neighborhood of interest, 10% of condos currently have a garden and 65% of houses have already had a garden. If a property randomly selected by Sarah has a garden, what is the probability of the property being a condo?(3 Points)

Answer 1

1)

P(X=2) =(₅C₂)*(0.35)²*(0.65)³ =0.3364

2)

P(X<10)=

∑x=09    (nCx)px(1−p)(n-x)    =

0.3575

3)

probability that the property is a condo WITHOUT a capacity of having a garden

=0.35*(1-0.1-0.08)=0.287

4)

P(condo |garden ) =0.35*0.1/0.65 =0.0538 (please try 0.0765 if this comes wrong and reply)