In simultaneous toss of 4 coins , what is the probability of getting exactly 3 heads ?

Answer

To solve the problem of finding the probability of getting exactly 3 heads when tossing 4 coins simultaneously, we can follow these steps:

### Step 1: Determine the total number of outcomes
When tossing a coin, there are 2 possible outcomes: heads (H) or tails (T). For 4 coins, the total number of outcomes can be calculated using the formula for the number of outcomes in a sequence of independent events:

\[ \text{Total Outcomes} = 2^n \]

where \( n \) is the number of coins tossed. Here, \( n = 4 \):

\[ \text{Total Outcomes} = 2^4 = 16 \]

### Step 2: Identify the favorable outcomes for getting exactly 3 heads
Next, we need to find the combinations that yield exactly 3 heads. The possible outcomes can be represented as follows:

1. HHHH
2. HHHT
3. HHTH
4. HTHH
5. THHH
6. HHTT
7. HTHT
8. THTH
9. HTTH
10. TTHH
11. THTT
12. HTTT
13. THTT
14. TTTT
15. TTTT
16. TTTT

From these outcomes, we can see that the combinations that yield exactly 3 heads are:

1. HHHT
2. HHTH
3. HTHH
4. THHH

Thus, there are 4 favorable outcomes.

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

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

Substituting the values we found:

\[ P(\text{exactly 3 heads}) = \frac{4}{16} = \frac{1}{4} \]

### Final Answer
Thus, the probability of getting exactly 3 heads when tossing 4 coins is:

\[ \frac{1}{4} \text{ or } 0.25 \]

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