A box contain 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, find the probability that it will be:
a blue card

Answer

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

### Step 1: Determine the total number of cards in the box.
- We have:
- 100 red cards
- 200 yellow cards
- 50 blue cards

**Calculation:**
Total number of cards = Number of red cards + Number of yellow cards + Number of blue cards
Total number of cards = 100 + 200 + 50 = 350

### Step 2: Identify the number of favorable outcomes.
- The favorable outcome in this case is drawing a blue card.
- We have 50 blue cards.

### Step 3: Use the probability formula.
- The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

**Substituting the values:**
\[ P(\text{blue card}) = \frac{\text{Number of blue cards}}{\text{Total number of cards}} = \frac{50}{350} \]

### Step 4: Simplify the fraction.
- To simplify \( \frac{50}{350} \):
- Both the numerator and the denominator can be divided by 50.

**Calculation:**
\[ \frac{50 \div 50}{350 \div 50} = \frac{1}{7} \]

### Final Answer:
The probability of drawing a blue card from the box is \( \frac{1}{7} \).

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