Out of 1000 small coloured bulbs `81^(3//2)` are of white colour `5^(3)` are red coloured ,` 2^(6)` are green coloured & rest are blue coloured .
What is the probability that bulb chosen is .
(i) blue coloured
(ii) red coloured
(iii) white coloured .

Answer

To solve the problem step by step, we need to find the number of bulbs of each color and then calculate the probabilities for blue, red, and white colored bulbs.

### Step 1: Calculate the number of white bulbs
We are given that the number of white bulbs is \( 81^{3/2} \).

- First, calculate \( 81^{1/2} \):
\[ 81^{1/2} = 9 \]
- Now, raise this result to the power of 3:
\[ 9^3 = 729 \]
Thus, the number of white bulbs is **729**.

### Step 2: Calculate the number of red bulbs
We are given that the number of red bulbs is \( 5^3 \).

- Calculate \( 5^3 \):
\[ 5^3 = 125 \]
Thus, the number of red bulbs is **125**.

### Step 3: Calculate the number of green bulbs
We are given that the number of green bulbs is \( 2^6 \).

- Calculate \( 2^6 \):
\[ 2^6 = 64 \]
Thus, the number of green bulbs is **64**.

### Step 4: Calculate the number of blue bulbs
To find the number of blue bulbs, we subtract the total number of white, red, and green bulbs from the total number of bulbs (1000).

- Total number of bulbs:
\[ \text{Total} = 1000 \]
- Total of white, red, and green bulbs:
\[ 729 + 125 + 64 = 918 \]
- Calculate the number of blue bulbs:
\[ \text{Blue bulbs} = 1000 - 918 = 82 \]
Thus, the number of blue bulbs is **82**.

### Step 5: Calculate the probabilities
Now, we can calculate the probabilities for each color of bulb.

#### (i) Probability of choosing a blue bulb
\[ P(\text{Blue}) = \frac{\text{Number of blue bulbs}}{\text{Total number of bulbs}} = \frac{82}{1000} \]
To simplify:
\[ P(\text{Blue}) = \frac{41}{500} \]

#### (ii) Probability of choosing a red bulb
\[ P(\text{Red}) = \frac{\text{Number of red bulbs}}{\text{Total number of bulbs}} = \frac{125}{1000} \]
To simplify:
\[ P(\text{Red}) = \frac{1}{8} \]

#### (iii) Probability of choosing a white bulb
\[ P(\text{White}) = \frac{\text{Number of white bulbs}}{\text{Total number of bulbs}} = \frac{729}{1000} \]

### Final Answers
- Probability of blue bulb: \( \frac{41}{500} \)
- Probability of red bulb: \( \frac{1}{8} \)
- Probability of white bulb: \( \frac{729}{1000} \)