Is Conditional Probability Influenced by Consecutivity

In summary, the probability of getting a specific sequence is independent of any previous rolls and the probability of getting a specific sequence is equal to the probability of getting any other sequence of the same length.
  • #1
kashmir0109
2
0
What I mean by this is,
Say I roll a die, given the specific condition that I get four eights consecutively such as
"8888",
the same probability as if I give the specific condition that I get another specific non-consecutive number such as?
"0248"

OR

Say I flip a quarter. Would the probability that I get HHHH in a row, the same as if I specify beforehand to get, say, HTHH?
 
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  • #2
I don't quite get your question. Are you asking whether the probability that you'll roll a particular sequence is dependent on what you've rolled previously? If so, the answer is no; see here,[/PLAIN] but also see the caveat here, which may be more relevant to your question.
 
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  • #3
kashmir0109 said:
What I mean by this is,
Say I roll a die, given the specific condition that I get four eights consecutively such as
"8888",
the same probability as if I give the specific condition that I get another specific non-consecutive number such as?
"0248"

OR

Say I flip a quarter. Would the probability that I get HHHH in a row, the same as if I specify beforehand to get, say, HTHH?

The answer to the second question is yes. I suspect it also true for the first, but yuou need to describe this peculiar die - are all numbers equally probable?
 

FAQ: Is Conditional Probability Influenced by Consecutivity

What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It represents the probability of one event happening based on the knowledge that another event has already occurred.

How does consecutivity affect conditional probability?

Consecutivity, or the order in which events occur, can influence conditional probability. In particular, the probability of an event occurring may change if the events are consecutive or occur in a specific order.

Can consecutivity increase or decrease conditional probability?

Yes, consecutivity can both increase or decrease conditional probability. This is because the likelihood of an event occurring can change based on the order in which events happen.

Is consecutivity the only factor that affects conditional probability?

No, there are other factors that can affect conditional probability such as the sample size, the independence of events, and the presence of other influencing variables. However, consecutivity is one factor that can have a significant impact on conditional probability.

How can we calculate conditional probability when consecutivity is a factor?

To calculate conditional probability when consecutivity is a factor, we can use the formula P(A|B) = P(A and B) / P(B), where A represents the event of interest and B represents the event that has already occurred. We can also use tree diagrams or contingency tables to visually represent the relationship between consecutivity and conditional probability.

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