If a coin is tossed four times then the probability of getting tails at least once is

Options

A. `1/16`
B. `15/16`
C. `13/16`
D. `11/16`

Answer

To solve the problem of finding the probability of getting tails at least once when a coin is tossed four times, we can follow these steps:

### Step 1: Determine the total number of outcomes when tossing a coin four times.
When a coin is tossed, there are 2 possible outcomes: heads (H) or tails (T). Therefore, if the coin is tossed four times, the total number of outcomes can be calculated as:
\[ \text{Total outcomes} = 2^4 = 16 \]

### Step 2: Identify the event of interest.
We want to find the probability of getting tails at least once in four tosses. Instead of calculating this probability directly, it is easier to first calculate the probability of the complementary event, which is getting no tails (i.e., getting all heads).

### Step 3: Calculate the probability of getting no tails (all heads).
The only way to get no tails in four tosses is to get heads in all four tosses. There is only one outcome that corresponds to this event: HHHH. Therefore, the probability of getting all heads (no tails) is:
\[ P(\text{No tails}) = \frac{\text{Number of favorable outcomes (all heads)}}{\text{Total outcomes}} = \frac{1}{16} \]

### Step 4: Calculate the probability of getting tails at least once.
Now, we can find the probability of getting tails at least once by subtracting the probability of getting no tails from 1:
\[ P(\text{At least one tail}) = 1 - P(\text{No tails}) = 1 - \frac{1}{16} = \frac{15}{16} \]

### Final Answer:
Thus, the probability of getting tails at least once when a coin is tossed four times is:
\[ \frac{15}{16} \]

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