In an experiment a coin is tossed 500 times. If the tail turns up 280 times, then find the probability of getting a head.

Options

A. `11/25`
B. `12/25`
C. `14/25`
D. `13/25`

Answer

To find the probability of getting a head when a coin is tossed 500 times and tails come up 280 times, we can follow these steps:

### Step 1: Determine the total number of tosses
The total number of times the coin is tossed is given as 500.

### Step 2: Calculate the number of heads
Since tails come up 280 times, we can find the number of heads by subtracting the number of tails from the total number of tosses:
\[ \text{Number of heads} = \text{Total tosses} - \text{Number of tails} \]
\[ \text{Number of heads} = 500 - 280 = 220 \]

### Step 3: Use the probability formula
The probability of an event is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (getting heads) is 220, and the total number of outcomes (total tosses) is 500.

### Step 4: Substitute the values into the formula
\[ \text{Probability of getting heads} = \frac{220}{500} \]

### Step 5: Simplify the fraction
To simplify \(\frac{220}{500}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20:
\[ \frac{220 \div 20}{500 \div 20} = \frac{11}{25} \]

### Final Answer
The probability of getting a head when the coin is tossed 500 times is \(\frac{11}{25}\).

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