Asked by Wallet Stack on Jul 11, 2024
Verified
If A and B are two independent events with P(A)= 0.9 and P(B|A)= 0.5,then P(A and B)= 0.45.
Independent Events
Two or more events that have no influence on each other's occurrence, meaning the happening of one does not affect the probability of the other.
Conditional Probability
The probability of an event occurring given that another event has already occurred, reflecting how the likelihood of an event can be affected by knowledge of another.
- Distinguish between independent and mutually exclusive events.
- Utilize the formula for the probability of the union and intersection of events.
Verified Answer
AJ
Amanda JonesJul 13, 2024
Final Answer :
True
Explanation :
Since A and B are independent, P(B|A) = P(B), and P(A and B) = P(A) * P(B). Given P(A) = 0.9 and P(B|A) = 0.5 implies P(B) = 0.5, thus P(A and B) = 0.9 * 0.5 = 0.45.
Learning Objectives
- Distinguish between independent and mutually exclusive events.
- Utilize the formula for the probability of the union and intersection of events.