4 coins are tossed . The probability that they are all heads is

Options

A. `(1)/(16)`
B. `(2)/(9)`
C. `(3)/(16)`
D. `(4)/(15)`

Answer

To find the probability that all four coins tossed show heads, we can follow these steps:

### Step 1: Determine the total number of outcomes when tossing 4 coins.
When a coin is tossed, it can land in one of two ways: heads (H) or tails (T). Therefore, for 4 coins, the total number of possible 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 tossed. Here, \( n = 4 \).

\[ \text{Total Outcomes} = 2^4 = 16 \]

### Step 2: Determine the number of favorable outcomes for getting all heads.
When we want to find the probability of getting all heads, we need to determine how many outcomes result in all coins showing heads. There is only one such outcome:

- HHHH (all four coins show heads)

Thus, the number of favorable outcomes is:

\[ \text{Favorable Outcomes} = 1 \]

### Step 3: Calculate the probability.
The probability \( P \) of an event is given by the formula:

\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]

Substituting the values we found:

\[ P(\text{All Heads}) = \frac{1}{16} \]

### Final Answer:
The probability that all four coins tossed are heads is:

\[ \frac{1}{16} \]

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