You are taking two courses this semoster and the probability thst you will ass c
ID: 3302985 • Letter: Y
Question
You are taking two courses this semoster and the probability thst you will ass counse A is 04, he The courses is 0.5 )What is the probability that you will pass course B b) What is the probability that you will pass course A given tht you passed usB c) What is the probability that you will pass course B given that you passed coune A d) Is the passing of the two courses independent event Use probbility inoation o jity your a e) Are the events of passing the courses mutiually esclusive Why or why notExplanation / Answer
Here we are given that the probability that we will pass course A is 0.4. Therefore P(A) = 0.4
P( both courses ) = 0.2
Also we are given that probability that we will pass at least one of the course is 0.5. This means:
P(A or B) = 0.5
a) Using addition law of probability we get:
P(A or B) = P(A) + P(B) - P( both courses )
Putting all the given values, we get:
0.5 = 0.4 + P(B) - 0.2
Therefore, P(B) = 0.5 - 0.4 + 0.2 = 0.3
Therefore probability of passing course B is 0.3
b) Given that we passed course B, the probability that we will pass course is A is given as: (Using Bayes theorem )
P( A | B) = P( both courses ) / P(B) = 0.2/0.3 = 0.6667
Therefore the required probability here is 0.6667
c) Given that we passed course A, the probability that we will pass course is B is given as: (Using Bayes theorem )
P( B | A) = P( both courses ) / P(A) = 0.2/0.4 = 0.5
Therefore the required probability here is 0.5
d) Here we have P(A) P(B) = 0.4*0.3 = 0.12
P( both courses ) = P(A and B) = 0.2
Therefore, P( both courses ) is not equal to P(A) P(B)
Therefore the passing of two courses is not independent.
e) P( both courses ) = P(A and B) = 0.2 which is not equal to 0.
Therefore the passing of two courses is not mutually exclusive.
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