If A and B are two mutually exclusive and exhaustive events and `P(B)=3/2P(A),` then find `P(A)`.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the properties of mutually exclusive and exhaustive events.
Mutually exclusive events cannot happen at the same time, and exhaustive events cover all possible outcomes. Therefore, for two mutually exclusive and exhaustive events A and B, we have:
\[ P(A) + P(B) = 1 \]

### Step 2: Use the given relationship between P(A) and P(B).
We are given that:
\[ P(B) = \frac{3}{2} P(A) \]
We can substitute this expression for P(B) into the equation from Step 1.

### Step 3: Substitute P(B) in the equation.
Substituting \( P(B) \) in the equation gives us:
\[ P(A) + \frac{3}{2} P(A) = 1 \]

### Step 4: Combine the terms.
Now, we can combine the terms on the left side:
\[ P(A) + \frac{3}{2} P(A) = \frac{2}{2} P(A) + \frac{3}{2} P(A) = \frac{5}{2} P(A) \]
So, we have:
\[ \frac{5}{2} P(A) = 1 \]

### Step 5: Solve for P(A).
To find \( P(A) \), we can multiply both sides by \( \frac{2}{5} \):
\[ P(A) = 1 \times \frac{2}{5} = \frac{2}{5} \]

### Conclusion:
Thus, the probability of event A is:
\[ P(A) = \frac{2}{5} \]

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