Answer :
Sure, let's go through the problem step-by-step to find the conditional probability [tex]\( P(F \mid E) \)[/tex].
Given:
- [tex]\( N(E \text{ and } F) = 220 \)[/tex]
- [tex]\( N(E) = 580 \)[/tex]
We are asked to find the conditional probability [tex]\( P(F \mid E) \)[/tex], which is defined as the probability of event [tex]\( F \)[/tex] occurring given that event [tex]\( E \)[/tex] has already occurred.
The formula for conditional probability is:
[tex]\[ P(F \mid E) = \frac{N(E \text{ and } F)}{N(E)} \][/tex]
Now, substituting the given values into the formula:
[tex]\[ P(F \mid E) = \frac{220}{580} \][/tex]
Evaluating this fraction gives:
[tex]\[ P(F \mid E) \approx 0.3793103448275862 \][/tex]
Therefore, the conditional probability [tex]\( P(F \mid E) \)[/tex] is approximately [tex]\( 0.3793 \)[/tex] or [tex]\( 37.93\% \)[/tex].
Given:
- [tex]\( N(E \text{ and } F) = 220 \)[/tex]
- [tex]\( N(E) = 580 \)[/tex]
We are asked to find the conditional probability [tex]\( P(F \mid E) \)[/tex], which is defined as the probability of event [tex]\( F \)[/tex] occurring given that event [tex]\( E \)[/tex] has already occurred.
The formula for conditional probability is:
[tex]\[ P(F \mid E) = \frac{N(E \text{ and } F)}{N(E)} \][/tex]
Now, substituting the given values into the formula:
[tex]\[ P(F \mid E) = \frac{220}{580} \][/tex]
Evaluating this fraction gives:
[tex]\[ P(F \mid E) \approx 0.3793103448275862 \][/tex]
Therefore, the conditional probability [tex]\( P(F \mid E) \)[/tex] is approximately [tex]\( 0.3793 \)[/tex] or [tex]\( 37.93\% \)[/tex].