Answer:
The value of P(A∩B) = 143/400 ⇒ answer D
Step-by-step explanation:
* Lets explain how to solve the problem
- P(B|A) is called the "Conditional Probability" of B given A
- Conditional probability is the probability of one event occurring
with some relationship to one or more other events
- That means event A has already happened, now what is the
chance of event B
- The formula for conditional probability is P(B|A) = P(A and B)/P(A)
- You can also write it as P(B|A) = P(A∩B)/P(A) because,
P(A and B) = P(A∩B)
∵ P(A) = 11/20
∵ P(B|A)= 13/20
∵ P(B|A) = P(A∩B)/P(A)
- Substitute the values of P(A) and P(B|A) in the rule
∴ 13/20 = P(A∩B)/(11/20)
- Multiply both sides by 11/20
∴ (13/20) × (11/20) = P(A∩B)
∴ 143/400 = P(A∩B)
* The value of P(A∩B) = 143/400
