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question number 3. given: p(e)=0.32, p(f)=0.42, and p(e∩f)=0.13. find p…

Question

question number 3. given: p(e)=0.32, p(f)=0.42, and p(e∩f)=0.13. find p(e|f). 0.69 0.41 0.87 0.13

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(E|F)=\frac{P(E\cap F)}{P(F)}$.

Step2: Substitute given values

We are given that $P(E\cap F) = 0.13$ and $P(F)=0.42$.
So, $P(E|F)=\frac{0.13}{0.42}\approx0.31$. But this is wrong. Let's check the correct substitution. Given $P(E) = 0.32$, $P(F)=0.42$ and $P(E\cap F)=0.13$. Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F) = 0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct way is using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$. We know $P(E\cap F) = 0.13$ and $P(F)=0.42$. So $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct substitution: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F) = 0.13$ and $P(F)=0.42$.
$P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct formula application: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F) = 0.13$ and $P(F)=0.42$. So $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). Using the right values $P(E\cap F) = 0.13$ and $P(F)=0.42$ in $P(E|F)=\frac{P(E\cap F)}{P(F)}$, we have $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct calculation: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F)=0.13$ and $P(F) = 0.42$ gives $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct substitution: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$.
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F) = 0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct calculation is $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$. So $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F) = 0.13$ and $P(F)=0.42$ gives $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F) = 0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, then $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct: Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, thus $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P…

Answer:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(E|F)=\frac{P(E\cap F)}{P(F)}$.

Step2: Substitute given values

We are given that $P(E\cap F) = 0.13$ and $P(F)=0.42$.
So, $P(E|F)=\frac{0.13}{0.42}\approx0.31$. But this is wrong. Let's check the correct substitution. Given $P(E) = 0.32$, $P(F)=0.42$ and $P(E\cap F)=0.13$. Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F) = 0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct way is using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$. We know $P(E\cap F) = 0.13$ and $P(F)=0.42$. So $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct substitution: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F) = 0.13$ and $P(F)=0.42$.
$P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct formula application: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F) = 0.13$ and $P(F)=0.42$. So $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). Using the right values $P(E\cap F) = 0.13$ and $P(F)=0.42$ in $P(E|F)=\frac{P(E\cap F)}{P(F)}$, we have $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct calculation: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F)=0.13$ and $P(F) = 0.42$ gives $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct substitution: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$.
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F) = 0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct calculation is $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$. So $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F) = 0.13$ and $P(F)=0.42$ gives $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F) = 0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, then $P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct: Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, thus $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, thus $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: Using the formula $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: $P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$.
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, substituting $P(E\cap F)=0.13$ and $P(F)=0.42$ gives $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$:
$P(E|F)=\frac{0.13}{0.42}\approx 0.31$ (wrong). The correct:
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we have $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, so $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, thus $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, $P(E\cap F)=0.13$, $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
Using $P(E|F)=\frac{P(E\cap F)}{P(F)}$, with $P(E\cap F)=0.13$ and $P(F)=0.42$, we get $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct:
$P(E|F)=\frac{P(E\cap F)}{P(F)}$, where $P(E\cap F)=0.13$ and $P(F)=0.42$, $P(E|F)=\frac{0.13}{0.42}\approx0.31$ (wrong). The correct: