If A and B are independent events with P(A) = 0.65 and P(A ∩ B)
= 0.26, so P(B) = _____________ SHOW ALL WORK!
general orientation
Concepts and reason
The problem deals with the concept of probability of independent events. The two events are said to be independent of each other when one event occurs, so it does not affect the second event. For example: tossing a coin.
Fundamentals
The probability formula for the two independent events is:
Here are two independent events.
Step by step
Step 1 of 2
The probability of occurrence of the event is.
The probability of the intersection of the two events is
So the probabilities are like and .
Using the probability formula for the two independent events, determine the probability of the event.
Step 2 of 2
Since the probability for the two independent events two is as:
Then the probability of the event will be,
Therefore, the probability of the event is.
Using the probability formula for the two independent events, the probability of the event is.
Beware of the terms independent events, dependent events, mutually exclusive events, etc. when solving the probability problem.
Answer
Therefore, the probability of the event is.
answer only
Therefore, the probability of the event is.
P(ANB)=P(A).P(B)
restoration
P(A)=0.65
restoration
P(ANB)=0.26
P(A)=0.65
P(ANB)=0.26
P(ANB)=P(A).P(B)
P(B)=P(ANB) P(A) 0.26 0.65 = 0.4
P(B)=0.4
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