1. Harry owns shares of stock in both Bidwell Value Company and Mini Car Motors

Question

1. Harry owns shares of stock in both Bidwell Value Company and Mini Car Motors Inc. Harry has recorded the performance of these shares on each day for a 200 day period as to whether the price has risen, fallen, or data is as follows: remained unchanged. Harry's Event Bidwell #ofda Rise Rise Rise Unchan Unchan Unchan Fall Fall Fall Mini Car Rise Unchanged Fall Rise Unchanged Fall Rise Unchanged Fall 40 20 18 12 Ed Es 28 Eg 38 What is the probability of a rise in Bidwell and a fall in Mini Car stock? (8 points) a. b. What is the probability of a rise in Bidwell or a fall in Mini Car stock? (8 points) Suppose Harry is told that Mini Car stock has fallen. What is the probability that Bidwell stock has risen? (7 points) c. d. Are the events "a rise in Bidwell stock" and "a fall in Mini Car stock" statistically independent? (7 points)

Explanation / Answer

a) probability of a rise in Bidwell and a fall in Mini Car stock =P(E3) =20/200 =0.1

b) probability=P(E1)+P(E2)+P(E3)+P(E6)+P(E9)=(40+14+20+14+38)/200 =0.63

c) probability that Bidwell stock has risen given Mini car stock has fallen =P(E3)/(P(E3)+P(E6)+P(E9))

=20/(20+14+38)=0.2778

d) P(Rise in Bidewell stock) =P(E1)+P(E2)+P(E3) =(40+14+20)/200=0.37

P(fall in Mini Car stck) =(P(E3)+P(E6)+P(E9)) =(20+14+38)/200=0.36

as P(Rise in Bidewell stock)*P(fall in Mini Car stck) =0.37*0.36 =0.1332 which is not equal to

P(Rise in Bidewell stock &fall in Mini Car stck)  

therefore not independent

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