A dice is thrown 100 times and the outcomes are noted as given below.When a dice is thrown at random, what is the probability of getting aQ(i) 3 (ii) 6 (iii) 4 (iv) 1

Answer

To solve the problem step-by-step, we will calculate the probability of getting each specified outcome when a die is thrown 100 times.

### Step 1: Understand the Total Outcomes
The total number of times the die is thrown is given as 100.

### Step 2: Find the Frequency of Each Outcome
We need to find out how many times each number (1, 3, 4, 6) appeared in the 100 throws. According to the video transcript:
- The number of times 3 appeared = 18
- The number of times 6 appeared = 9
- The number of times 4 appeared = 15
- The number of times 1 appeared = 21

### Step 3: Calculate the Probability of Each Outcome
The probability of an event is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]

#### (i) Probability of getting a 3
- Number of times 3 appeared = 18
- Total outcomes = 100
\[ P(3) = \frac{18}{100} = \frac{9}{50} \]

#### (ii) Probability of getting a 6
- Number of times 6 appeared = 9
- Total outcomes = 100
\[ P(6) = \frac{9}{100} \]

#### (iii) Probability of getting a 4
- Number of times 4 appeared = 15
- Total outcomes = 100
\[ P(4) = \frac{15}{100} = \frac{3}{20} \]

#### (iv) Probability of getting a 1
- Number of times 1 appeared = 21
- Total outcomes = 100
\[ P(1) = \frac{21}{100} \]

### Summary of Probabilities
- Probability of getting a 3: \( \frac{9}{50} \)
- Probability of getting a 6: \( \frac{9}{100} \)
- Probability of getting a 4: \( \frac{3}{20} \)
- Probability of getting a 1: \( \frac{21}{100} \)