Two coins are tossed simultaneously 125 times and it was observed that both head appeared 15 times. If two coins are tossed simultaneously at random, what is the probability of getting both heads?

Answer

To solve the problem, we need to find the probability of getting both heads when two coins are tossed simultaneously. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We are given that two coins are tossed 125 times, and both heads appeared 15 times. We need to calculate the probability of getting both heads.

### Step 2: Define the Terms
- **n(E)**: Number of favorable outcomes (getting both heads)
- **n(S)**: Total number of trials (total tosses)

### Step 3: Identify the Values
From the problem:
- n(E) = 15 (the number of times both heads appeared)
- n(S) = 125 (the total number of times the coins were tossed)

### Step 4: Use the Probability Formula
The probability of an event is given by the formula:
\[ P(E) = \frac{n(E)}{n(S)} \]

### Step 5: Substitute the Values
Now, we substitute the values we identified:
\[ P(E) = \frac{15}{125} \]

### Step 6: Simplify the Fraction
To simplify the fraction:
\[ P(E) = \frac{15 \div 5}{125 \div 5} = \frac{3}{25} \]

### Step 7: Conclusion
Thus, the probability of getting both heads when two coins are tossed is:
\[ P(E) = \frac{3}{25} \]