Suppose six coins are tossed simultaneously. Then the probability of getting at least one tail is

Options

A. `71/72`
B. `53/54`
C. `63/64`
D. `1/12`

Answer

To solve the problem of finding the probability of getting at least one tail when tossing six coins, we can follow these steps:

### Step 1: Determine the Total Outcomes
When tossing a coin, there are 2 possible outcomes: heads (H) or tails (T). Therefore, when tossing 6 coins simultaneously, the total number of outcomes can be calculated using the formula for the total outcomes of independent events:

\[ \text{Total Outcomes} = 2^n \]

where \( n \) is the number of coins. In this case, \( n = 6 \).

\[ \text{Total Outcomes} = 2^6 = 64 \]

### Step 2: Determine the Favorable Outcomes
To find the probability of getting at least one tail, it is easier to first calculate the probability of the complementary event, which is getting no tails at all (i.e., all heads).

The only outcome where there are no tails is when all coins show heads. There is only 1 such outcome (HHHHHH).

### Step 3: Calculate the Number of Favorable Outcomes
Now, we can find the number of favorable outcomes for getting at least one tail by subtracting the number of outcomes with no tails from the total outcomes:

\[ \text{Favorable Outcomes} = \text{Total Outcomes} - \text{Outcomes with No Tails} \]

\[ \text{Favorable Outcomes} = 64 - 1 = 63 \]

### Step 4: Calculate the Probability
The probability of getting at least one tail can now be calculated using the formula:

\[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} \]

Substituting the values we found:

\[ \text{Probability} = \frac{63}{64} \]

### Final Answer
Thus, the probability of getting at least one tail when tossing six coins is:

\[ \frac{63}{64} \]