SOLUTION: Let B and C be two events such that P(B)=0.01 and P(C)=0.70. Do not round your responses. (a) Determine P(B∪C), given that B and C are independent. (b) Determine P(B∪C)

Algebra ->  Probability-and-statistics -> SOLUTION: Let B and C be two events such that P(B)=0.01 and P(C)=0.70. Do not round your responses. (a) Determine P(B∪C), given that B and C are independent. (b) Determine P(B∪C)      Log On


   

Question 1188669: Let B and C be two events such that P(B)=0.01 and P(C)=0.70.
Do not round your responses.
(a) Determine P(B∪C), given that B and C are independent.
(b) Determine P(B∪C), given that B and C are mutually exclusive.
Found 2 solutions by Shin123, ikleyn:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
a) Since B and C are independent events, we can just multiply the probabilities together, 0.70%2A0.01=0.007
b) By definition since B and C are mutually exclusive both cannot happen at the same time, so the answer is 0.

Answer by ikleyn(52834) About Me  (Show Source):
You can put this solution on YOUR website!
.


            Both answers by tutor @shin123 are incorrect.
            I came to bring a correct solution. 


(a)     P(B U C) = P(B + P(C) - P(B and C).


     Since the events B and C are independent, P(B and C) = P(B)*P(C) = 0.01*0.7 = 0.007.


     Then  P(B U C) = P(B) + P(C) - P(B and C) = 0.01 + 0.7 - 0.007 = 0.703.     ANSWER



(b)  Since the events B and C are mutually exclusive,  P(B U C) = P(B) + P(C) = 0.01 + 0.7 = 0.71.    ANSWER

Solved (correctly)