Let A and B be dependent (i.e., not independent) events. Which of the following

Question

Let A and B be dependent (i.e., not independent) events. Which of the following is always true? A) P(A|B) = 0 B) P(A|B) lessthanorequalto P(A) C) P(A|B) = 1 D) P(A intersection B) lessthanorequalto P(A|B) E) None of these is necessarily true. A certain device has a 3% defective rate. An inspector randomly picks 20 of the devices from a shipment. What is the probability that there will be at least one defective item among the 20? A) (20 1) .03 (.97)^19 (B) 1 - (.97)^20 C) 1 - (20 1) .03 (.97)^19 D) (20 1) (.03)^19 (.97) E) 1 - (.03)^20 The probability that a patient recovers from a rare blood disease is 40%. Fifteen people are to have this disease currently. What is the probability that exactly 5 recover? A) (15 5) (.4)^5 (.6)^10 B) (15 10) (.4)^10 (.6)^5 C) 1 - sigma^4 _i = 1 (15 i) (.4)^i (.6)^15 - i D) (15 5) (.6)^5 (.4)^10 E) None of the above The probability that a regularly scheduled flight departs on time is P(D) = .83; the regularly scheduled flight arrives on time is P(A) = .82. The probability that a regularly flight both arrives and departs on time is .78 What is the probability that a regularly scheduled flight arrives on time, given that it time? A) .78/.83 B) .78/.82 C) (.83) (.82) D) (.78) (.83) E) None of the above

Explanation / Answer

1. If A and B are dependent events, then P(B|A)=P(A intersection B)/P(A), and P(A)+P(B)=1, therefore, option E is correct.

2. This accounts for binomial distribution with number of trials, n=20, probability of success, p=0.03, and speciifc r number of success in n trials. Assume X denote the r.v number of defective items. Use formula, P(X,r)=nCr(p)^r(1-p)^n-r.

P(X>=1)=1-P(X<1)=1-P(X=0)=1-20C0(0.03)^0(0.97)^20=1-(0.97)^20 [B is correct]

3. This too accounts for binomial distribution, with n=15, p=0.4, and r=5.

P(X>=5)=1-P(X<5)=1-P(X<=4)=1-sigma i=1 to 4 (15 C i)(0.4)^i (0.6)^15-i [C is correct]

4. Assume events A and D are not independent, P(A|D)=P(D intersection A)/P(D)=0.78/0.83 [A is correct]

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