In an experiment , 2 unbiased coins were tossed for 200 times. During the experiment, two heads were received 25 times, one head was received 100 times and no head was received 75 times. Calculate the probability of each event on the basis of the experiment.

Answer

To solve the problem of calculating the probabilities of different outcomes when tossing two unbiased coins 200 times, we can follow these steps:

### Step 1: Identify the total number of trials
The total number of times the coins were tossed is given as 200.

### Step 2: Identify the outcomes and their frequencies
From the experiment, we have the following outcomes:
- Two heads (HH) were received 25 times.
- One head (HT or TH) was received 100 times.
- No heads (TT) were received 75 times.

### Step 3: Calculate the probability of getting two heads
The probability of an event is calculated using the formula:
\[ \text{Probability of an event} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} \]

For two heads (event E1):
\[ P(E1) = \frac{\text{Number of times two heads were received}}{\text{Total trials}} = \frac{25}{200} = \frac{1}{8} \]

### Step 4: Calculate the probability of getting one head
For one head (event E2):
\[ P(E2) = \frac{\text{Number of times one head was received}}{\text{Total trials}} = \frac{100}{200} = \frac{1}{2} \]

### Step 5: Calculate the probability of getting no heads
For no heads (event E3):
\[ P(E3) = \frac{\text{Number of times no heads were received}}{\text{Total trials}} = \frac{75}{200} = \frac{3}{8} \]

### Step 6: Summarize the probabilities
Now we can summarize the probabilities of each event:
- Probability of getting two heads (P(E1)): \(\frac{1}{8}\)
- Probability of getting one head (P(E2)): \(\frac{1}{2}\)
- Probability of getting no heads (P(E3)): \(\frac{3}{8}\)

### Final Answer:
- P(E1) = \(\frac{1}{8}\)
- P(E2) = \(\frac{1}{2}\)
- P(E3) = \(\frac{3}{8}\)

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