CA Foundation Exam  >  CA Foundation Questions  >  Given that for two events A and B, P(A)=3/5, ... Start Learning for Free
Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?
  • a)
    0.655
  • b)
    13/60
  • c)
    31/60
  • d)
    0.775
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B)...
P(A|B) = P(A&B)/P(B)
So first we have to find P(A&B)
P(AUB) = P(A) + P(B) - P(A&B)3/4 = 3/5 + 2/3 - P(A&B)
Multiply through by 60
45 = 36 + 40 - 60P(A&B)
45 = 76 - 60P(A&B)
-31 = -60P(A&B)
31/60 = P(A&B)
Go back to 
P(A|B) = P(A&B)/P(B)
P(A|B) = (31/60)/(2/3)
P(A|B) = (31/60)(3/2)
P(A|B) = 31/40 = 0.775
View all questions of this test
Most Upvoted Answer
Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B)...
Given:
- P(A) = 3/5
- P(B) = 2/3
- P(A union B) = 3/4

To find: P(A|B)

Solution:
We can use the formula for conditional probability: P(A|B) = P(A intersection B) / P(B)

Step 1: Find P(A intersection B)
We know that P(A union B) = P(A) + P(B) - P(A intersection B)
Substituting the given values, we get:
3/4 = 3/5 + 2/3 - P(A intersection B)
Simplifying, we get:
P(A intersection B) = 1/15

Step 2: Find P(A|B)
Using the formula for conditional probability, we get:
P(A|B) = P(A intersection B) / P(B)
Substituting the values we found in Step 1, we get:
P(A|B) = (1/15) / (2/3)
Simplifying, we get:
P(A|B) = 0.775

Therefore, the correct answer is option D (0.775).
Explore Courses for CA Foundation exam
Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer?
Question Description
Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer?.
Solutions for Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation. Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Given that for two events A and B, P(A)=3/5, P(B)=2/3 and P(A union B) =3/4, what is P(A|B)?a)0.655b)13/60c)31/60d)0.775Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
Explore Courses for CA Foundation exam

Top Courses for CA Foundation

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev