Two coins are tossed simultaneously 200 times and we get
two heads: 58 times, one head: 83 times, 0 head: 59 times
When two coins are tossed at random, what is the probability of getting
Q (i) 2 heads
(ii) 1 head
(iii) 0 head

Answer

To solve the problem, we need to find the probability of getting two heads, one head, and zero heads when two coins are tossed simultaneously 200 times. We have the following data from the experiment:

- Two heads (HH): 58 times
- One head (HT or TH): 83 times
- Zero heads (TT): 59 times

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

### Step 1: Probability of getting 2 heads
The probability of an event is calculated using the formula:

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

For the event of getting 2 heads (HH):

- Number of favorable outcomes = 58 (the number of times we got 2 heads)
- Total number of outcomes = 200 (the total number of times the coins were tossed)

So, the probability of getting 2 heads is:

\[ P(\text{2 heads}) = \frac{58}{200} \]

Now, simplify the fraction:

\[ P(\text{2 heads}) = \frac{58 \div 2}{200 \div 2} = \frac{29}{100} \]

### Step 2: Probability of getting 1 head
For the event of getting 1 head (HT or TH):

- Number of favorable outcomes = 83 (the number of times we got 1 head)
- Total number of outcomes = 200

So, the probability of getting 1 head is:

\[ P(\text{1 head}) = \frac{83}{200} \]

### Step 3: Probability of getting 0 heads
For the event of getting 0 heads (TT):

- Number of favorable outcomes = 59 (the number of times we got 0 heads)
- Total number of outcomes = 200

So, the probability of getting 0 heads is:

\[ P(\text{0 heads}) = \frac{59}{200} \]

### Summary of Results
- Probability of getting 2 heads: \( \frac{29}{100} \)
- Probability of getting 1 head: \( \frac{83}{200} \)
- Probability of getting 0 heads: \( \frac{59}{200} \)