A coin is tossed 200 times and it was found that head appears 72 times and tail appears 128 times. If a coin is tossed at random, what is the probabiltity of getting (i) a head (ii) a tail?

Answer

To solve the problem step by step, we will calculate the probability of getting a head and a tail when a coin is tossed 200 times.

### Step 1: Understand the Problem
We know that a coin is tossed 200 times, resulting in 72 heads and 128 tails. We need to find the probability of getting a head and the probability of getting a tail.

### Step 2: Define the Events
Let:
- \( E_1 \) be the event of getting a head.
- \( E_2 \) be the event of getting a tail.

### Step 3: Total Number of Trials
The total number of trials (tosses) is:
\[ n(S) = 200 \]

### Step 4: Number of Favorable Outcomes for Heads
The number of favorable outcomes for getting a head is:
\[ n(E_1) = 72 \]

### Step 5: Calculate the Probability of Getting a Head
The probability of getting a head, denoted as \( P(E_1) \), is calculated using the formula:
\[ P(E_1) = \frac{n(E_1)}{n(S)} \]
Substituting the values:
\[ P(E_1) = \frac{72}{200} \]

### Step 6: Simplify the Probability of Getting a Head
To simplify \( \frac{72}{200} \):
1. Divide both the numerator and the denominator by 8:
\[ \frac{72 \div 8}{200 \div 8} = \frac{9}{25} \]
Thus, the probability of getting a head is:
\[ P(E_1) = \frac{9}{25} \]

### Step 7: Number of Favorable Outcomes for Tails
The number of favorable outcomes for getting a tail is:
\[ n(E_2) = 128 \]

### Step 8: Calculate the Probability of Getting a Tail
The probability of getting a tail, denoted as \( P(E_2) \), is calculated using the formula:
\[ P(E_2) = \frac{n(E_2)}{n(S)} \]
Substituting the values:
\[ P(E_2) = \frac{128}{200} \]

### Step 9: Simplify the Probability of Getting a Tail
To simplify \( \frac{128}{200} \):
1. Divide both the numerator and the denominator by 8:
\[ \frac{128 \div 8}{200 \div 8} = \frac{16}{25} \]
Thus, the probability of getting a tail is:
\[ P(E_2) = \frac{16}{25} \]

### Final Results
- The probability of getting a head is \( \frac{9}{25} \).
- The probability of getting a tail is \( \frac{16}{25} \).