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?

Question

Accepted Answer

To determine the probability of getting a tail when a coin is tossed, we need to consider the total number of tosses and the number of times a tail was obtained.

1. **Total Tosses**: The coin was tossed 130 times.
2. **Heads Obtained**: Heads were obtained 75 times.

To find the number of tails obtained, we subtract the number of heads from the total number of tosses:

$$ \text{Number of tails} = \text{Total tosses} - \text{Number of heads} = 130 - 75 = 55 $$

The probability of getting a tail is calculated by dividing the number of tails by the total number of tosses:

$$ \text{Probability of getting a tail} = \frac{\text{Number of tails}}{\text{Total tosses}} = \frac{55}{130} $$

Thus, the correct probability of getting a tail is $\frac{55}{130}$, which corresponds to **Option 3**.

**Explanation of why other options are incorrect:**

- **Option 1 (75/130)**: This represents the probability of getting a head, not a tail. Since heads were obtained 75 times out of 130 tosses, this fraction is incorrect for tails.

- **Option 2 (130/75)**: This fraction is not a valid probability because it is greater than 1. Probabilities must be between 0 and 1.

- **Option 4 (130/55)**: Similar to Option 2, this fraction is greater than 1 and cannot represent a probability. Additionally, it does not relate to the number of tails obtained.

Therefore, based on the calculations and logical reasoning, **Option 3 (55/130)** is the correct answer for the probability of getting a tail.