Probability Unions: Solving Problems

In summary, the conversation was about finding the probabilities of success for two independent actors, with a given probability of success of 0.95. The probability that both actors are successful is calculated to be 0.9025, while the probability that neither actor is successful is 0.0025. Another method for calculating this probability is suggested, using the fact that the chance of an actor not being successful is 0.05. The probability that either actor is successful is found to be 0.9975. Feedback on the calculations is appreciated.
  • #1
cue928
130
0
Have a problem that I've worked through, would appreciate any feedback on it to tell if I'm doing it correctly:

Say the probability of success is .95. Two different actors, acting independently:
1. Probability that both actors are successful: I had P(A intersect B) = P(A) * P(B) = (.95)*(.95) = .9025

2. Probability that neither actor is successful? Was a little confused on this one, but I thought it would be P(A U B)'. In (3), I'd calculated the P(A U B) to be .9975, so 1-.9975 = .0025

3. Probability that either actor is successful? I used P(A U B) = P(A) + P(B) - P(A intersect B) = .9975

thank you much.
 
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  • #2
Looks pretty good to me!
 
  • #3
Looks ok!

May I suggest another method for (2)?? The chance that an auther is not successful is 0.05. so the chance that neither author iss successful is 0.05*0.05 by independence.
 

FAQ: Probability Unions: Solving Problems

What is a probability union?

A probability union is a mathematical concept that represents the likelihood of two or more events occurring together. It is denoted by the symbol "∪" and is read as "union".

How do you calculate a probability union?

The probability of a union can be calculated using the formula P(A∪B) = P(A) + P(B) - P(A∩B), where P(A) and P(B) are the individual probabilities of events A and B, and P(A∩B) is the probability of both events occurring together.

What is the difference between a probability union and an intersection?

A probability union represents the likelihood of events occurring together, while an intersection represents the likelihood of events occurring separately. In other words, a union includes the probability of either event happening, while an intersection only includes the probability of both events happening.

When should you use a probability union to solve a problem?

A probability union should be used when you want to find the probability of at least one of two or more events occurring. This is often useful in real-world scenarios where multiple outcomes are possible, such as in gambling or insurance.

What are some common mistakes to avoid when using probability unions?

One common mistake is assuming that the probability of a union is simply the sum of the individual probabilities. It is important to remember to subtract the probability of the intersection of events to avoid double-counting. Additionally, make sure to properly identify which events are being included in the union and which are not.

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