A coin is tossed 750 times with the following frequencies: Head: 500, Tail : 250
Compute the probability for each event

Answer

To compute the probability of getting heads and tails when a coin is tossed 750 times, we can follow these steps:

### Step 1: Identify the total number of tosses
The total number of times the coin is tossed is given as 750.

### Step 2: Identify the frequency of heads and tails
From the problem, we know:
- Frequency of Heads = 500
- Frequency of Tails = 250

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

For heads:
- Favorable outcomes = Frequency of Heads = 500
- Total outcomes = Total number of tosses = 750

So, the probability of getting heads (P(H)) is:
\[ P(H) = \frac{500}{750} \]

### Step 4: Simplify the probability of heads
To simplify \( \frac{500}{750} \):
- Divide both the numerator and the denominator by 250:
\[ P(H) = \frac{500 \div 250}{750 \div 250} = \frac{2}{3} \]

### Step 5: Calculate the probability of getting tails
Using the same formula for tails:
- Favorable outcomes = Frequency of Tails = 250
- Total outcomes = Total number of tosses = 750

So, the probability of getting tails (P(T)) is:
\[ P(T) = \frac{250}{750} \]

### Step 6: Simplify the probability of tails
To simplify \( \frac{250}{750} \):
- Divide both the numerator and the denominator by 250:
\[ P(T) = \frac{250 \div 250}{750 \div 250} = \frac{1}{3} \]

### Final Results
- Probability of Heads (P(H)) = \( \frac{2}{3} \)
- Probability of Tails (P(T)) = \( \frac{1}{3} \)

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