If E and F are two events associated with a random experiment for which P(E)=0.6, `P(E uu F)=0.85` and `P(E nn F)`=0.42 , then P(F) is

Options

A. `0.6`
B. `0.67`
C. `0.7`
D. `0.73`

Answer

To find \( P(F) \), we can use the formula for the probability of the union of two events. The formula is given by:

\[ P(E \cup F) = P(E) + P(F) - P(E \cap F) \]

### Step 1: Write down the known values
We have the following values from the problem:
- \( P(E) = 0.6 \)
- \( P(E \cup F) = 0.85 \)
- \( P(E \cap F) = 0.42 \)

### Step 2: Substitute the known values into the formula
Now, we can substitute these values into the union formula:

\[ 0.85 = 0.6 + P(F) - 0.42 \]

### Step 3: Simplify the equation
Now, we simplify the equation:

\[ 0.85 = 0.6 - 0.42 + P(F) \]

Calculating \( 0.6 - 0.42 \):

\[ 0.6 - 0.42 = 0.18 \]

So the equation becomes:

\[ 0.85 = 0.18 + P(F) \]

### Step 4: Solve for \( P(F) \)
To find \( P(F) \), we rearrange the equation:

\[ P(F) = 0.85 - 0.18 \]

Calculating \( 0.85 - 0.18 \):

\[ P(F) = 0.67 \]

### Conclusion
Thus, the probability of event \( F \) is:

\[ P(F) = 0.67 \]