Need help conditional probability

In summary, the conversation discusses the probability of an airplane returning within certain time intervals based on past records. The question is asked about the probability of the airplane returning in 30 minutes and 40 minutes given that it has not returned in 20 minutes. The formula for conditional probability is mentioned but the person is stuck on how to apply it in this scenario. The hint is given to consider simplifications in the formula, such as the probability of the plane not returning in 20 minutes.
  • #1
lehaihua
1
0
hi all,
I have a question that i really want to know the answer.

the probability that an airplane will return in 10min is 30%, in 20min is 30%, in 30min is 0%,
in 40min is 40% according to the past history records. given that the airplane has not return
in 20min, what is the probability that the airplane will return in 30 min and in 40 min?

i really stuck on this question since the formula doesn't seem to work[P(a|b) = P(a and b)/P(a)]

please give me some hint!thx thx
 
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  • #2
Your formula should work perfectly well, you just need a little thought to work out what your a and b should be in this case.
What is the probability that the plane does not return in 20 minutes?
If it returns in e.g 30 minutes then clearly it doesn't return in 10 minutes, so P(30 mins and not 10 mins)=P(30 mins), what other simplifications can you make?
 
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1. What is conditional probability?

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred. It is used to calculate the probability of an event taking place under certain conditions.

2. How is conditional probability calculated?

Conditional probability is calculated by dividing the probability of the intersection of two events by the probability of the event that is already known to have occurred. This can be represented as P(A|B) = P(A∩B)/P(B), where A is the event we are interested in and B is the event that has already occurred.

3. What is the difference between conditional and unconditional probability?

Unconditional probability is the probability of an event occurring without any prior knowledge or conditions, while conditional probability takes into account a known condition or event that has already occurred. Conditional probability is always equal to or less than the unconditional probability.

4. How is conditional probability used in real life?

Conditional probability is used in a variety of fields, such as finance, healthcare, and insurance, to assess risk and make predictions. It is also commonly used in data analysis and machine learning to make informed decisions based on available data.

5. Can you give an example of conditional probability?

One example of conditional probability is the probability of a student passing a test given that they have studied for it. The probability of passing the test would be higher if the student has studied compared to if they have not studied, making it a conditional probability.

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