Three coins are tossed simultaneously. What is the probability that they will fall two heads and one tail?

Options

A. `1//3`
B. `1//2`
C. `1//4`
D. `3//8`

Answer

To solve the problem of finding the probability of getting two heads and one tail when three coins are tossed simultaneously, we can follow these steps:

### Step 1: Determine the Sample Space
When three coins are tossed, each coin can either land on heads (H) or tails (T). The total number of outcomes can be calculated as follows:

- Each coin has 2 outcomes (H or T).
- For 3 coins, the total number of outcomes = 2^3 = 8.

The sample space (S) consists of the following outcomes:
1. HHH
2. HHT
3. HTH
4. THH
5. HTT
6. THT
7. TTH
8. TTT

### Step 2: Identify the Favorable Outcomes
Next, we need to find the outcomes that result in exactly two heads and one tail. The favorable outcomes are:
1. HHT
2. HTH
3. THH

Thus, there are 3 favorable outcomes.

### Step 3: Calculate the Probability
The probability (P) of an event is given by the formula:

\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case:
- Number of favorable outcomes = 3 (HHT, HTH, THH)
- Total number of outcomes = 8

So, the probability of getting two heads and one tail is:

\[ P(\text{2 heads, 1 tail}) = \frac{3}{8} \]

### Final Answer
The probability that when three coins are tossed, they will show two heads and one tail is \( \frac{3}{8} \).

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