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Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E∩F) = 0.3, then what will be the value of P(F|E)?
- a)2/5
- b)3/5
- c)3/4
- d)2/4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E...
We know that P(F|E) = P(E∩F) / P(E). (By formula for conditional probability)
Value of P(E∩F) is given to be 0.3 and value of P(E) is given to be 0.5.
P(F|E) = (0.3) / (0.5).
P(F|E) = 3 / 5.
Value of P(E∩F) is given to be 0.3 and value of P(E) is given to be 0.5.
P(F|E) = (0.3) / (0.5).
P(F|E) = 3 / 5.
Most Upvoted Answer
Given that E and F are events such that P(E) = 0.5, P(F) = 0.4 and P(E...
Given that E and F are events such that P(E) = 0.5, P(F) = 0.4, and P(E ∩ F) = 0.2, we can find P(E' ∩ F') using the complement rule.
The complement rule states that P(A') = 1 - P(A) for any event A.
First, we need to find P(E' ∪ F'). We can use the inclusion-exclusion principle:
P(E' ∪ F') = P(E') + P(F') - P(E' ∩ F')
Since E and F are events, their complements are also events. Therefore, we can rewrite the equation as:
P(E' ∪ F') = 1 - P(E) + 1 - P(F) - P(E' ∩ F')
Now let's substitute the given values:
P(E' ∪ F') = 1 - 0.5 + 1 - 0.4 - P(E' ∩ F')
Simplifying further:
P(E' ∪ F') = 1.1 - P(E' ∩ F')
Now, we need to find P(E' ∩ F'). We can use the formula:
P(E' ∩ F') = 1 - P(E ∪ F)
Since E and F are events, their complements are also events. Therefore, we can rewrite the equation as:
P(E' ∩ F') = 1 - (P(E) + P(F) - P(E ∩ F))
Now let's substitute the given values:
P(E' ∩ F') = 1 - (0.5 + 0.4 - 0.2)
Simplifying further:
P(E' ∩ F') = 1 - 0.7
P(E' ∩ F') = 0.3
Now we can substitute this value back into the equation for P(E' ∪ F'):
P(E' ∪ F') = 1.1 - 0.3
P(E' ∪ F') = 0.8
Therefore, P(E' ∩ F') = 0.3 and P(E' ∪ F') = 0.8.
The complement rule states that P(A') = 1 - P(A) for any event A.
First, we need to find P(E' ∪ F'). We can use the inclusion-exclusion principle:
P(E' ∪ F') = P(E') + P(F') - P(E' ∩ F')
Since E and F are events, their complements are also events. Therefore, we can rewrite the equation as:
P(E' ∪ F') = 1 - P(E) + 1 - P(F) - P(E' ∩ F')
Now let's substitute the given values:
P(E' ∪ F') = 1 - 0.5 + 1 - 0.4 - P(E' ∩ F')
Simplifying further:
P(E' ∪ F') = 1.1 - P(E' ∩ F')
Now, we need to find P(E' ∩ F'). We can use the formula:
P(E' ∩ F') = 1 - P(E ∪ F)
Since E and F are events, their complements are also events. Therefore, we can rewrite the equation as:
P(E' ∩ F') = 1 - (P(E) + P(F) - P(E ∩ F))
Now let's substitute the given values:
P(E' ∩ F') = 1 - (0.5 + 0.4 - 0.2)
Simplifying further:
P(E' ∩ F') = 1 - 0.7
P(E' ∩ F') = 0.3
Now we can substitute this value back into the equation for P(E' ∪ F'):
P(E' ∪ F') = 1.1 - 0.3
P(E' ∪ F') = 0.8
Therefore, P(E' ∩ F') = 0.3 and P(E' ∪ F') = 0.8.
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