the probability that a particular treatment will be effective is p=.31. the prob

Question

the probability that a particular treatment will be effective is p=.31. the probability the particular treatment will not be effective is 9= .69.

A.what is the relationship do this probability have

18. A psychologist determines that the probabil- ity of relapse in her clinic is p .12. Assuming independent outcomes, what is the probability that two of her patients relapse? 19. The probability that a particular treatment will be effective is p = .31. The probability that a particular treatment will not be effective is q = .69. la) What type of relationship do these proba- bilities have? Ib) What is the probability that the treatment will be or will not be effective? psychologist states that there is a 5% chance n05 that his decision will be wrong.

Explanation / Answer

Ans:

19)

a)These are Complementry events,as both events add upto 1.

Complementary events are mutually exclusive, but when combined make the entire sample space.

Let

A=particular treatment will be effective

A'=particular treatment will not be effective

P(A)+P(A')=0.69+0.31=1

i.e. P(A')=1-P(A)

b)P(treatment will be or will not be effective)=P(A or A')

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

=P(A)+P(A')-0

=1

(i.e atleast one of the event either will be effective or will not be effective will occur certainly)

18)P(two patients relapse)=0.12*0.12=0.0144

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