Find P(B): Solving Probability Formula 1

In summary, to find P(B), we use the formula P(A|B)=P(AnB)/P(B) and solve algebraically for P(B). When substituting values, we get P(B)=0.6/0.1=6, which is impossible since probabilities cannot be larger than 1. Double check if the problem was given correctly.
  • #1
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1. Given P(AnB)=0.6 and P(A|B)=0.10, find P(B)



2. P(A|B)=P(AnB)/P(B)




3. I plugged in the numbers in the formula but keep getting that P(B) is 6... which is wrong since P cannot be greater than 0. Am I doing something wrong?
 
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  • #2
Instead of plugging in numbers, solve this equation algebraically for P(B):
P(A|B)=P(AnB)/P(B)

When you have P(B) isolated, substitute the values you have for the two other quantities.
 
  • #3
That's what I did.

P(B)=P(AnB)/P(A|B)=0.6/0.1=6...but this makes no sense to me.
 
  • #4
I don't see anything wrong in your work, although obviously a probability can't be larger than 1. Are you sure you have the problem written the same as it was given to you?
 

1. What is the formula for finding P(B)?

The formula for finding P(B) is P(B) = number of favorable outcomes / total number of possible outcomes.

2. How do I know which outcomes are favorable in P(B)?

To determine the favorable outcomes, you need to identify the events that satisfy the given condition or criteria in the problem. These events will be considered as favorable outcomes for P(B).

3. Can you give an example of solving P(B) using the probability formula?

Yes, for example, if we have a bag with 10 red marbles and 5 blue marbles, and we want to find the probability of selecting a red marble, the formula would be P(red) = 10/15 = 2/3.

4. What do I do if the problem involves more than one event for P(B)?

If the problem involves multiple events, you can use the formula P(B) = P(A) x P(A|B), where P(A) is the probability of event A occurring and P(A|B) is the probability of event A occurring given that event B has already occurred.

5. How do I interpret the result of P(B)?

The result of P(B) represents the likelihood or chance of event B occurring. It is expressed as a decimal, percentage, or fraction between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

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