$$ 1 \leftarrow \begin{array}{l} ext { If } P(E)=0.50, P(E ext { or } F)=0.80 ext {, and } P(E ext { and } F)=0.05 ext {, find } P(F) ext {. } \ P(F)=\square ext { (Simplify your answer.) }\end{array} $$

Question

$$ 1 \leftarrow \begin{array}{l}	ext { If } P(E)=0.50, P(E 	ext { or } F)=0.80 	ext {, and } P(E 	ext { and } F)=0.05 	ext {, find } P(F) 	ext {. } \ P(F)=\square 	ext { (Simplify your answer.) }\end{array} $$

UpStudy AI · Accepted Answer

To find $$ P(F) $$, we can use the formula for the probability of the union of two events:

$$
P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)
$$

We are given the following values:

- $$ P(E) = 0.50 $$
- $$ P(E \text{ or } F) = 0.80 $$
- $$ P(E \text{ and } F) = 0.05 $$

Substituting these values into the formula, we have:

$$
0.80 = 0.50 + P(F) - 0.05
$$

Now, simplify the equation:

$$
0.80 = 0.50 - 0.05 + P(F)
$$
$$
0.80 = 0.45 + P(F)
$$

Next, isolate $$ P(F) $$:

$$
P(F) = 0.80 - 0.45
$$
$$
P(F) = 0.35
$$

Thus, the value of $$ P(F) $$ is

$$
\boxed{0.35}
$$
$$ P(F) = 0.35 $$

\( 1 \leftarrow \begin{array}{l}\text { If } P(E)=0.50, P(E \text { or } F)=0.80 \text {, and } P(E \text { and } F)=0.05 \text {, find } P(F) \text {. } \\ P(F)=\square \text { (Simplify your answer.) }\end{array} \)

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