पाँच सिक्कों को एक साथ उछाला जाता है तब सभी सिक्कों पर चित्त (शीर्ष) आने की प्रायिकता क्या होगी?

Options

A. `(1)/(32)`
B. `(1)/(16)`
C. `(1)/(64)`
D. `(1)/(2)`

Answer

To find the probability of getting heads (चित्त) on all five coins when tossed together, we can follow these steps:

### Step 1: Understand the total outcomes
When we toss a single coin, there are two possible outcomes: heads (H) or tails (T). Therefore, when we toss five coins, the total number of outcomes can be calculated using the formula for the total outcomes of independent events.

**Total Outcomes = 2^n**, where n is the number of coins.

For 5 coins:
\[ \text{Total Outcomes} = 2^5 = 32 \]

### Step 2: Determine the favorable outcomes
Next, we need to find the number of favorable outcomes for getting heads on all five coins. There is only one way to get heads on all five coins, which is HHHHH.

**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:
\[ P(\text{All Heads}) = \frac{1}{32} \]

### Final Answer
The probability of getting heads on all five coins when tossed together is:
\[ \frac{1}{32} \]

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