A box contains 2 blue caps, 4 red caps, 5 green caps and 1 yellow cap.
If one cap is picked at random, what is the probability that it is either blue or yellow ?

Options

A. `2/9`
B. `1/4`
C. `3/8`
D. `6/11`

Answer

To find the probability that a randomly picked cap from the box is either blue or yellow, we can follow these steps:

### Step 1: Determine the total number of caps in the box.
- The box contains:
- 2 blue caps
- 4 red caps
- 5 green caps
- 1 yellow cap

**Total caps = 2 (blue) + 4 (red) + 5 (green) + 1 (yellow) = 12 caps**

### Step 2: Identify the favorable outcomes.
- We want to find the probability of picking either a blue or a yellow cap.
- The number of blue caps = 2
- The number of yellow caps = 1

**Total favorable outcomes = 2 (blue) + 1 (yellow) = 3 caps**

### Step 3: Calculate the probability.
- Probability is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

- Substituting the values we found:

\[ \text{Probability} = \frac{3 \text{ (favorable outcomes)}}{12 \text{ (total outcomes)}} = \frac{3}{12} \]

### Step 4: Simplify the probability.
- We can simplify \(\frac{3}{12}\):

\[ \frac{3}{12} = \frac{1}{4} \]

### Conclusion:
The probability that the cap picked is either blue or yellow is \(\frac{1}{4}\).

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