If A and B are independent events with P(A) = 0.65 and P(A ∩ B)

= 0.26, then P(B) = _____________ SHOW ALL WORK!

General guidance

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 then it does not affect the second event. For example: tossing a coin.

Fundamentals

The formula of the probability for the two independent two event is:

Here are two independent events.

Step-by-step

Step 1 of 2

The probability of occurring of event is.

The probability of intersection of the two events is

Therefore the probabilities are as and .

Using the formula of the probability for the two independent two event determine the probability of event.

Step 2 of 2

Since the probability for the two independent two event is as:

Then the probability of the event will be,

Therefore, the probability of the event is.

Using the formula of the probability for the two independent two event the probability of the event is.

Beware of the terms independent events, dependent events, mutually exclusive events etc. while 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)

A&B

P(A)=0.65

A&B

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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