A coin is tossed 130 times and head is obtained 75 times. If a coin is tossed at random, what is the probability of getting a tail?

Options

A. A)`(75)/(130)`
B. B)`(130)/(75)`
C. C)`(55)/(130)`
D. D)`(130)/(55)`

Answer

To find the probability of getting a tail when a coin is tossed, 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 130.

### Step 2: Determine the number of heads obtained
The number of heads obtained is given as 75.

### Step 3: Calculate the number of tails obtained
To find the number of tails, we subtract the number of heads from the total number of tosses:
\[ \text{Number of tails} = \text{Total tosses} - \text{Number of heads} = 130 - 75 = 55 \]

### Step 4: Calculate the probability of getting a tail
The probability of an event is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the favorable outcome is getting a tail, which we found to be 55. The total number of outcomes is 130.
\[ \text{Probability of getting a tail} = \frac{\text{Number of tails}}{\text{Total tosses}} = \frac{55}{130} \]

### Step 5: Simplify the probability (if necessary)
The fraction \(\frac{55}{130}\) can be simplified. Both the numerator and the denominator can be divided by 5:
\[ \frac{55 \div 5}{130 \div 5} = \frac{11}{26} \]

Thus, the probability of getting a tail when a coin is tossed is \(\frac{11}{26}\).

### Final Answer
The probability of getting a tail is \(\frac{55}{130}\) or simplified to \(\frac{11}{26}\).

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