In one toss of two coins together find the probability of getting:
(i) two tails
(ii) one head and one tail

Explanation

To solve the problem of finding the probability of getting two tails and one head and one tail when tossing two coins, we can follow these steps:

### Step 1: Identify the Sample Space
When tossing two coins, the possible outcomes (sample space) can be listed as follows:
- HH (both coins show heads)
- HT (first coin shows heads, second coin shows tails)
- TH (first coin shows tails, second coin shows heads)
- TT (both coins show tails)

Thus, the sample space \( S \) is:
\[ S = \{ HH, HT, TH, TT \} \]

### Step 2: Count the Total Outcomes
From the sample space, we can see that there are a total of 4 outcomes.

### Step 3: Calculate the Probability of Getting Two Tails
To find the probability of getting two tails (TT), we identify the number of favorable outcomes for this event. There is only 1 favorable outcome (TT).

The probability \( P \) of getting two tails is given by the formula:
\[ P(\text{two tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
\[ P(\text{two tails}) = \frac{1}{4} \]

### Step 4: Calculate the Probability of Getting One Head and One Tail
Next, we need to find the probability of getting one head and one tail. The favorable outcomes for this event are HT and TH. Thus, there are 2 favorable outcomes.

Using the same probability formula:
\[ P(\text{one head and one tail}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
\[ P(\text{one head and one tail}) = \frac{2}{4} = \frac{1}{2} \]

### Summary of Results
- The probability of getting two tails is \( \frac{1}{4} \).
- The probability of getting one head and one tail is \( \frac{1}{2} \).