A coin is tossed four times. The probability that atleast one heads turns up is

Options

A. `(1)/(16)`
B. `(1)/(8)`
C. `(7)/(8)`
D. `(15)/(16)`

Answer

To solve the problem of finding the probability that at least one head turns up when a coin is tossed four times, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Total Outcomes**:
When a coin is tossed, there are 2 possible outcomes: Heads (H) or Tails (T). If we toss the coin 4 times, the total number of outcomes can be calculated as:
\[ \text{Total Outcomes} = 2^4 = 16 \]

2. **Calculate the Probability of No Heads**:
To find the probability of getting at least one head, it is easier to first calculate the probability of getting no heads at all (i.e., getting tails every time). The only outcome where no heads appear is when we get Tails in all 4 tosses (TTTT). There is only 1 such outcome.
\[ \text{Favorable Outcomes for No Heads} = 1 \]

3. **Calculate the Probability of No Heads**:
The probability of getting no heads (all tails) can be calculated as:
\[ P(\text{No Heads}) = \frac{\text{Favorable Outcomes for No Heads}}{\text{Total Outcomes}} = \frac{1}{16} \]

4. **Calculate the Probability of At Least One Head**:
The probability of getting at least one head is the complement of the probability of getting no heads. Thus, we can use the formula:
\[ P(\text{At Least One Head}) = 1 - P(\text{No Heads}) = 1 - \frac{1}{16} \]
\[ P(\text{At Least One Head}) = \frac{16}{16} - \frac{1}{16} = \frac{15}{16} \]

5. **Final Answer**:
Therefore, the probability that at least one head turns up when a coin is tossed four times is:
\[ \frac{15}{16} \]