If A and B are events such that `P(A)=0.42, P(B)=0.48` and P(A and B)=0.6. Determine
(i) P (not A) (ii) P (A or B).

Answer

To solve the problem step by step, we will determine \( P(\text{not } A) \) and \( P(A \text{ or } B) \) using the given probabilities.

### Given:
- \( P(A) = 0.42 \)
- \( P(B) = 0.48 \)
- \( P(A \cap B) = 0.6 \)

### Step 1: Calculate \( P(\text{not } A) \)

The probability of the complement of an event \( A \) (i.e., \( P(\text{not } A) \)) can be calculated using the formula:
\[ P(\text{not } A) = 1 - P(A) \]

Substituting the value of \( P(A) \):
\[ P(\text{not } A) = 1 - 0.42 = 0.58 \]

### Step 2: Calculate \( P(A \text{ or } B) \)

The probability of the union of two events \( A \) and \( B \) (i.e., \( P(A \cup B) \)) can be calculated using the formula:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Substituting the values:
\[ P(A \cup B) = 0.42 + 0.48 - 0.6 \]

Calculating the sum:
\[ P(A \cup B) = 0.90 - 0.6 = 0.30 \]

### Final Answers:
(i) \( P(\text{not } A) = 0.58 \)
(ii) \( P(A \text{ or } B) = 0.30 \)

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