Question

Furniture dealers know that when a man walks in alone, they make a sale 5% of the time; when a woman walks in alone, they make a sale 15% of the time, but when a man and woman walk in together, they make a sale 30% of the time. When the front door opens, 90% of the time a woman enters, either alone or with a man, and 40% of the time a man enters, either alone or with a woman. Let S={sale}, M={man walks in}, and W={woman walks in}

What is the probability that a man and woman enter together?

Each time the door opens, find

If a sale is made, find the probability that the sale was made to a man that entered alone.

Are {Man walks in} and {Woman walks in} independent?

Answer 1

1) probability that a man and woman enter together=P(men and woman walks in)

=P(man walks in )+P(women walks in )-1 =0.4+0.9-1=0.3

2)

probability of sale =P(sale)=P(man walks alone and sale+woman walks alone and sale+both walk and sale)

=(0.4-0.3)*0.05+(0.9-0.3)*0.15+0.3*0.3=0.185

therefore probability that the sale was made to a man that entered alone given sales made

=P(man walks alone and sale)/P(sale) =(0.4-0.3)*0.05/0.185=0.027027

as P(man walks in )*P(women walks in) is not equal to P(man and women walks in) theefore not independent

  

answered by: anonymous