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For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3?
Most Upvoted Answer
For two independent events A and B, what is P (A B), given P(A)=3/5 an...
When 2 events are independent then
p(AB)=P(A)×P(B)
=3/5×2/3
=6/15
= 0.4
p(AB)=P(A)×P(B)
=3/5×2/3
=6/15
= 0.4
Community Answer
For two independent events A and B, what is P (A B), given P(A)=3/5 an...
P(A B) for Independent Events
When dealing with two independent events A and B, the probability of both events occurring, denoted as P(A ∩ B), can be calculated using the multiplication rule for independent events.
Understanding Independence
- Events A and B are independent if the occurrence of one does not affect the occurrence of the other.
- This means that P(A | B) = P(A) and P(B | A) = P(B).
Formula for Independent Events
- The probability of both events A and B happening together is calculated as:
P(A ∩ B) = P(A) × P(B)
Given Probabilities
- We have:
- P(A) = 3/5
- P(B) = 2/3
Calculating P(A ∩ B)
- Substitute the given probabilities into the formula:
P(A ∩ B) = (3/5) × (2/3)
- Perform the multiplication:
- Numerator: 3 × 2 = 6
- Denominator: 5 × 3 = 15
- Therefore,
P(A ∩ B) = 6/15
- Simplifying the fraction:
P(A ∩ B) = 2/5
Final Answer
Thus, the probability of both events A and B occurring together is:
P(A ∩ B) = 2/5
When dealing with two independent events A and B, the probability of both events occurring, denoted as P(A ∩ B), can be calculated using the multiplication rule for independent events.
Understanding Independence
- Events A and B are independent if the occurrence of one does not affect the occurrence of the other.
- This means that P(A | B) = P(A) and P(B | A) = P(B).
Formula for Independent Events
- The probability of both events A and B happening together is calculated as:
P(A ∩ B) = P(A) × P(B)
Given Probabilities
- We have:
- P(A) = 3/5
- P(B) = 2/3
Calculating P(A ∩ B)
- Substitute the given probabilities into the formula:
P(A ∩ B) = (3/5) × (2/3)
- Perform the multiplication:
- Numerator: 3 × 2 = 6
- Denominator: 5 × 3 = 15
- Therefore,
P(A ∩ B) = 6/15
- Simplifying the fraction:
P(A ∩ B) = 2/5
Final Answer
Thus, the probability of both events A and B occurring together is:
P(A ∩ B) = 2/5
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For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3?
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For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3? 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 For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3?.
For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3? 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 For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For two independent events A and B, what is P (A B), given P(A)=3/5 and P(B)=2/3?.
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