Let S and T are two events difined on a sample space with probabilities
`P(S)=0.5,P(T)=069,P(S//T)=0.5`
The value of P(S or T) is

Options

A. `0.6900`
B. `1.19`
C. `0.8450`
D. 0

Explanation

To find the value of \( P(S \cup T) \) (the probability of S or T), we can use the following formula:

\[ P(S \cup T) = P(S) + P(T) - P(S \cap T) \]

### Step 1: Identify Given Values
We are given:
- \( P(S) = 0.5 \)
- \( P(T) = 0.69 \)
- \( P(S | T) = 0.5 \)

### Step 2: Calculate \( P(S \cap T) \)
We know that:

\[ P(S | T) = \frac{P(S \cap T)}{P(T)} \]

From this, we can rearrange to find \( P(S \cap T) \):

\[ P(S \cap T) = P(S | T) \times P(T) \]

Substituting the known values:

\[ P(S \cap T) = 0.5 \times 0.69 = 0.345 \]

### Step 3: Substitute Values into the Union Formula
Now we can substitute \( P(S) \), \( P(T) \), and \( P(S \cap T) \) into the union formula:

\[ P(S \cup T) = P(S) + P(T) - P(S \cap T) \]

Substituting the values we have:

\[ P(S \cup T) = 0.5 + 0.69 - 0.345 \]

### Step 4: Perform the Calculation
Now, calculate:

1. First, add \( P(S) \) and \( P(T) \):

\[ 0.5 + 0.69 = 1.19 \]

2. Then subtract \( P(S \cap T) \):

\[ 1.19 - 0.345 = 0.845 \]

Thus, the value of \( P(S \cup T) \) is:

\[ P(S \cup T) = 0.845 \]

### Final Answer
The value of \( P(S \cup T) \) is \( 0.845 \).

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