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Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F) then value of P(S|F)is __________
- a)0
- b)-1
- c)1
- d)2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let E and F be events of a sample space S of an experiment, if P(S|F) ...
Explanation: We know that P(S|F) = P(S∩F) / P(F). (By formula for conditional probability)
Which is equivalent to P(F) / P(F) = 1, hence the value of P(S|F) = 1.
Which is equivalent to P(F) / P(F) = 1, hence the value of P(S|F) = 1.
Community Answer
Let E and F be events of a sample space S of an experiment, if P(S|F) ...
Explanation:
Given: P(S|F) = P(F|F)
We need to find the value of P(S|F).
Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which is read as "the probability of A given B".
In our case, we are given P(S|F) = P(F|F). This means the probability of event S occurring given that event F has occurred is equal to the probability of event F occurring given that event F has occurred.
Application of Bayes' Theorem:
Bayes' theorem relates conditional probabilities to calculate the probability of an event given prior knowledge or information.
The formula for Bayes' theorem is:
P(A|B) = (P(B|A) * P(A)) / P(B)
In our case, we can rewrite the given expression as:
P(S|F) = P(F|F)
Using Bayes' theorem, we can rearrange this expression as:
P(S|F) = (P(F|S) * P(S)) / P(F)
Simplifying:
Since P(F|F) is equal to 1 (the probability of an event occurring given that the event has already occurred is always 1), we can substitute this value in the equation:
P(S|F) = (P(F|S) * P(S)) / P(F)
P(S|F) = (P(F|S) * P(S)) / 1
P(S|F) = P(F|S) * P(S)
Conclusion:
From the above equation, we can conclude that P(S|F) is equal to P(F|S) * P(S).
Since P(F|S) is the probability of event F occurring given that event S has occurred, and P(S) is the probability of event S, the value of P(S|F) is equal to P(F|S) * P(S), which is 1.
Therefore, the correct answer is option 'C' - 1.
Given: P(S|F) = P(F|F)
We need to find the value of P(S|F).
Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which is read as "the probability of A given B".
In our case, we are given P(S|F) = P(F|F). This means the probability of event S occurring given that event F has occurred is equal to the probability of event F occurring given that event F has occurred.
Application of Bayes' Theorem:
Bayes' theorem relates conditional probabilities to calculate the probability of an event given prior knowledge or information.
The formula for Bayes' theorem is:
P(A|B) = (P(B|A) * P(A)) / P(B)
In our case, we can rewrite the given expression as:
P(S|F) = P(F|F)
Using Bayes' theorem, we can rearrange this expression as:
P(S|F) = (P(F|S) * P(S)) / P(F)
Simplifying:
Since P(F|F) is equal to 1 (the probability of an event occurring given that the event has already occurred is always 1), we can substitute this value in the equation:
P(S|F) = (P(F|S) * P(S)) / P(F)
P(S|F) = (P(F|S) * P(S)) / 1
P(S|F) = P(F|S) * P(S)
Conclusion:
From the above equation, we can conclude that P(S|F) is equal to P(F|S) * P(S).
Since P(F|S) is the probability of event F occurring given that event S has occurred, and P(S) is the probability of event S, the value of P(S|F) is equal to P(F|S) * P(S), which is 1.
Therefore, the correct answer is option 'C' - 1.
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Let E and F be events of a sample space S of an experiment, if P(S|F) = P(F|F) then value of P(S|F)is __________a)0b)-1c)1d)2Correct answer is option 'C'. Can you explain this answer?
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