SOLUTION: The probability John buys a car is .3 and the probability that Jane buys a car is .2. However if John buys a new car the probability Jane buys a car is .4. Are the purchases excl

Question 1162606: The probability John buys a car is .3 and the probability that Jane buys a car is .2. However if John buys a new car the probability Jane buys a car is .4.
Are the purchases exclusive?
Are the purchases independent?
What is the probability that both buy a car?
What is the probability that a least one buys a car?
What is the probability neither buys a car?
Answer by ikleyn(52873) (Show Source): You can put this solution on YOUR website!
.


First statement says that  P(John) = 0.3  and  P(Jane) = 0.2.


The second statement is about the conditional probability. It says


    P(John and Jane) / P(John) = 0.4,  or, equivalently,


    P(John and Jane) = 0.3*0.4 = 0.12.


Now I am ready to answer questions.



(a)  To answer this question, we must compare  P(John and Jane)  with  P(John)*P(Jane).


     P(John and JAne) = 0.12, as we saw above;  P(John)*P(Jane) = 0.3*0.2 = 0.06.


     ANSWER.  These events are NOT independent.




(b)  I just found this value:  P(John and Jane) = 0.12.




(c)  P(John or Jane) = P(John) + P(Jane) - P(John and Jane) = 0.3 + 0.2 - 0.12.


     You complete this calculation.



(d)  This probability is the complement to (c).

I answered all the questions.

Solved.

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