A bag contains 5 blue gems, 8 red gems and 2 green gems . A gem is drawn at random . What is the probability of getting a blue gem ?

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(2)/(9)`
D. `(5)/(6)`

Answer

To find the probability of drawing a blue gem from the bag, we can follow these steps:

### Step 1: Identify the number of blue gems.
The bag contains 5 blue gems.

### Step 2: Calculate the total number of gems in the bag.
To find the total number of gems, we add the number of blue, red, and green gems together:
- Number of blue gems = 5
- Number of red gems = 8
- Number of green gems = 2

Total number of gems = Number of blue gems + Number of red gems + Number of green gems
Total number of gems = 5 + 8 + 2 = 15

### Step 3: Write the formula for probability.
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

### Step 4: Substitute the values into the probability formula.
Here, the number of favorable outcomes (drawing a blue gem) is 5, and the total number of outcomes (total gems) is 15.
\[ \text{Probability of getting a blue gem} = \frac{5}{15} \]

### Step 5: Simplify the fraction.
To simplify \(\frac{5}{15}\), we divide both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{5 \div 5}{15 \div 5} = \frac{1}{3} \]

### Final Answer:
The probability of getting a blue gem is \(\frac{1}{3}\).

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