Threecoins are tossed once. Find the probability of getting
(i) 3 heads (ii) 2 heads
(iii) 3 tails.

Answer

To solve the problem of finding the probability of getting 3 heads, 2 heads, and 3 tails when tossing three coins, we can follow these steps:

### Step 1: Determine the Sample Space
When tossing 3 coins, each coin has 2 possible outcomes: Heads (H) or Tails (T). The total number of outcomes when tossing 3 coins can be calculated as:
\[ \text{Total Outcomes} = 2^n = 2^3 = 8 \]
The sample space (S) consists of the following outcomes:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT

### Step 2: Calculate the Probability of Getting 3 Heads (HHH)
To find the probability of getting 3 heads, we identify the favorable outcomes. There is only 1 outcome where all coins show heads:
- HHH

Thus, the probability \( P(3 \text{ heads}) \) is given by:
\[ P(3 \text{ heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{8} \]

### Step 3: Calculate the Probability of Getting 2 Heads
Next, we count the outcomes with exactly 2 heads. The favorable outcomes are:
- HHT
- HTH
- THH

There are 3 outcomes where there are exactly 2 heads. Therefore, the probability \( P(2 \text{ heads}) \) is:
\[ P(2 \text{ heads}) = \frac{3}{8} \]

### Step 4: Calculate the Probability of Getting 3 Tails (TTT)
Finally, we find the probability of getting 3 tails. There is only 1 outcome where all coins show tails:
- TTT

Thus, the probability \( P(3 \text{ tails}) \) is:
\[ P(3 \text{ tails}) = \frac{1}{8} \]

### Summary of Probabilities
- Probability of getting 3 heads: \( P(3 \text{ heads}) = \frac{1}{8} \)
- Probability of getting 2 heads: \( P(2 \text{ heads}) = \frac{3}{8} \)
- Probability of getting 3 tails: \( P(3 \text{ tails}) = \frac{1}{8} \)