Two coins are tossed simultaneously 400 times and we get
two heads : 180 times
one head : 148 times
no head : 72 times .
If two coins are tossed at random , what is the probability of getting
(i) 2 heads ? (ii) 1 head ? (iii) 0 head ?

Options

A. `0.45` , `0.37` , `0.18`
B. `0.47` , `0.27` , `0.13`
C. `0.40` , `0.30` , `0.10`
D. `0.65` , `0.67` , `0.68`

Explanation

To solve the problem, we need to calculate the probabilities of getting 2 heads, 1 head, and 0 heads when two coins are tossed simultaneously. We have the following data from the experiment:

- Total tosses = 400
- Number of times 2 heads occurred = 180
- Number of times 1 head occurred = 148
- Number of times 0 heads occurred = 72

Now, let's calculate the probabilities step by step.

### Step 1: Calculate the probability of getting 2 heads
The probability \( P(2 \text{ heads}) \) is given by the formula:

\[ P(2 \text{ heads}) = \frac{\text{Number of times 2 heads occurred}}{\text{Total tosses}} \]

Substituting the values:

\[ P(2 \text{ heads}) = \frac{180}{400} \]

Now, simplify the fraction:

\[ P(2 \text{ heads}) = \frac{180 \div 20}{400 \div 20} = \frac{9}{20} \]

### Step 2: Calculate the probability of getting 1 head
The probability \( P(1 \text{ head}) \) is given by:

\[ P(1 \text{ head}) = \frac{\text{Number of times 1 head occurred}}{\text{Total tosses}} \]

Substituting the values:

\[ P(1 \text{ head}) = \frac{148}{400} \]

Now, simplify the fraction:

\[ P(1 \text{ head}) = \frac{148 \div 4}{400 \div 4} = \frac{37}{100} \]

### Step 3: Calculate the probability of getting 0 heads
The probability \( P(0 \text{ heads}) \) is given by:

\[ P(0 \text{ heads}) = \frac{\text{Number of times 0 heads occurred}}{\text{Total tosses}} \]

Substituting the values:

\[ P(0 \text{ heads}) = \frac{72}{400} \]

Now, simplify the fraction:

\[ P(0 \text{ heads}) = \frac{72 \div 8}{400 \div 8} = \frac{9}{50} \]

### Final Results
Now we can summarize the probabilities:

1. Probability of getting 2 heads: \( P(2 \text{ heads}) = \frac{9}{20} \)
2. Probability of getting 1 head: \( P(1 \text{ head}) = \frac{37}{100} \)
3. Probability of getting 0 heads: \( P(0 \text{ heads}) = \frac{9}{50} \)