In determining what size inventories of two products to have on hand before prom

Question

In determining what size inventories of two products to have on hand before promoting the sales of one product. it is important to know if sales of the two products are independent Given that the probability that a customer will buy product A is 6, and the probability that a customer writ buy product B is 4, and the probability that a customer will buy either product A or B or both a 7; determine if the sales of the two products are dependent or independent A security system has two subsystems either of which can dial the police department m the event of a break m Subsystem A uses ultrasonic waves to detect the presence of a foreign body Subsystem B employs switches at al windows and doors If an intrusion occurs, the probability that it will be detected by A is.95 and by B a.90 and by both systems.89 If there a an intrusion what a the probability that it will be detected by devices A or B or both? What is the probability that the system won't detect the intrusion?

Explanation / Answer

2.Given that P(A or B)=0.7

Or P(A)+P(B)-P(A and B)=0.7

Or 0.6+0.4-P(A and B)=0.7

Or -P(A and B)=0.7-0.6-0.4

Or P(A and B)=0.3

Now, P(A)*P(B)=0.6*0.4=0.24 which s not equal to P(A and B).

Thus the two sales products are not independent.

3.a)P(A or B or both)

=P(A union B)

=P(A)+P(B)-P(A and B)

=0.95+0.90-0.89

=0.96

b)The probability that the system won’t detect intrusion is 1-0.96=0.4

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