Two coins are tossed simultaneously for 360 times. The number of times '2 Tails' appeared was three times 'No Tail' appeared and number of times '1 Tail' appeared is double the number of times 'No Tail' appeared. Find the probability of getting 'Two tails'.

Options

A. `1//2`
B. `1//3`
C. `1//4`
D. `1//5`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define Variables
Let:
- \( x \) = Number of times 'No Tail' appeared.
- Therefore, the number of times '2 Tails' appeared = \( 3x \) (as given in the problem).
- The number of times '1 Tail' appeared = \( 2x \) (as given in the problem).

### Step 2: Set Up the Equation
According to the problem, the total number of outcomes when tossing the coins is 360. Therefore, we can write the equation:
\[ x + 2x + 3x = 360 \]

### Step 3: Simplify the Equation
Combine the terms on the left side:
\[ 6x = 360 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 6 to find \( x \):
\[ x = \frac{360}{6} = 60 \]

### Step 5: Find the Number of Times Each Outcome Occurred
Now that we have \( x \):
- Number of times 'No Tail' appeared = \( x = 60 \)
- Number of times '1 Tail' appeared = \( 2x = 2 \times 60 = 120 \)
- Number of times '2 Tails' appeared = \( 3x = 3 \times 60 = 180 \)

### Step 6: Calculate the Probability of Getting 'Two Tails'
The probability \( P \) of getting 'Two Tails' is given by the formula:
\[ P(\text{Two Tails}) = \frac{\text{Number of times 'Two Tails' appeared}}{\text{Total outcomes}} = \frac{180}{360} \]

### Step 7: Simplify the Probability
Now simplify the fraction:
\[ P(\text{Two Tails}) = \frac{180}{360} = \frac{1}{2} \]

### Final Answer
Thus, the probability of getting 'Two Tails' is \( \frac{1}{2} \).

---