SOLUTION: Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45 Find P(J AND K). Find the probability of the complement of event (J AND K). Find the probability of the c

Algebra ->  Probability-and-statistics -> SOLUTION: Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45 Find P(J AND K). Find the probability of the complement of event (J AND K). Find the probability of the c      Log On


   

Question 1201670: Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45
Find P(J AND K).

Find the probability of the complement of event (J AND K).

Find the probability of the complement of event (J OR K).
Answer by ikleyn(52778) About Me  (Show Source):
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Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45
Find P(J AND K).
Find the probability of the complement of event (J AND K).
Find the probability of the complement of event (J OR K).
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Start from this probability IDENTITY, which is valid for all/every/each events 

    P(J or K) = P(J) + P(K) - P(J and K).


Substitute here the given values.  You will get 

    0.45 = 0.18 + 0.37 - P(J and K).


From this equation, find  P(J and K)

    P(J and K) = 0.18 + 0.37 - 0.45 = 0.1.


ANSWER.  P(J and K) = 0.1.

Solved.


To get the complementary probability, subtract the base probability from 1.