The probability that atleast one of the events A and B occurs is 0.6 If A and B occur simulataneously with probability 0.2, then `Poverset(-)((A))+Poverset(-)((B))` is equal to

Options

A. `0.4`
B. `0.8`
C. `1.2`
D. `1.6`

Explanation

To solve the problem step by step, we will use the information provided and apply the relevant probability formulas.

### Step 1: Understand the given information
We are given:
- The probability that at least one of the events A and B occurs, denoted as \( P(A \cup B) \), is 0.6.
- The probability that both events A and B occur simultaneously, denoted as \( P(A \cap B) \), is 0.2.

### Step 2: Use the formula for the union of two events
The formula for the probability of the union of two events is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the known values into this formula:
\[ 0.6 = P(A) + P(B) - 0.2 \]

### Step 3: Rearrange the equation to find \( P(A) + P(B) \)
Now, we can rearrange the equation to find \( P(A) + P(B) \):
\[ P(A) + P(B) = 0.6 + 0.2 = 0.8 \]

### Step 4: Express \( P(A) \) and \( P(B) \) in terms of their complements
We know that:
\[ P(A) = 1 - P(A') \]
\[ P(B) = 1 - P(B') \]
where \( P(A') \) and \( P(B') \) are the probabilities of the complements of A and B, respectively.

### Step 5: Substitute the expressions for \( P(A) \) and \( P(B) \)
Substituting these expressions into the equation we found in Step 3:
\[ (1 - P(A')) + (1 - P(B')) = 0.8 \]
This simplifies to:
\[ 2 - (P(A') + P(B')) = 0.8 \]

### Step 6: Solve for \( P(A') + P(B') \)
Rearranging gives:
\[ P(A') + P(B') = 2 - 0.8 = 1.2 \]

### Final Answer
Thus, the value of \( P(A') + P(B') \) is:
\[ \boxed{1.2} \]