Three coins are tossed simultaneously 180 times and it is found that 3 tails appeared 34 times, 2 tails appeared 55 times, 1 tail appeared 72 times and no tail appeared 19 times. Find the probability of getting
3 tails

Answer

To find the probability of getting 3 tails when three coins are tossed, we can follow these steps:

### Step 1: Identify the number of favorable outcomes
From the problem, we know that 3 tails appeared 34 times when the coins were tossed. Therefore, the number of favorable outcomes for getting 3 tails is:
- Favorable outcomes = 34

### Step 2: Identify the total number of outcomes
The total number of times the coins were tossed is given as 180. Therefore, the total number of outcomes is:
- Total outcomes = 180

### Step 3: Use the probability formula
The probability (P) of an event is calculated using the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we identified:
\[ P(\text{3 tails}) = \frac{34}{180} \]

### Step 4: Simplify the fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 34 and 180 is 2.
- Dividing both by 2:
\[ P(\text{3 tails}) = \frac{34 \div 2}{180 \div 2} = \frac{17}{90} \]

### Final Answer
Thus, the probability of getting 3 tails when three coins are tossed is:
\[ \frac{17}{90} \]

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