A large basket of fruits contains 3 oranges, 2 apples and 5 bananas. If a piece of fruit is chosen at random, what is the probability of getting an orange or a banana?

Options

A. `(7)/(8)`
B. `(1)/(5)`
C. `(4)/(5)`
D. `(1)/(2)`

Answer

To find the probability of getting an orange or a banana from a basket containing 3 oranges, 2 apples, and 5 bananas, we can follow these steps:

### Step 1: Determine the total number of fruits in the basket.
- We have:
- Oranges: 3
- Apples: 2
- Bananas: 5

**Total number of fruits = Number of oranges + Number of apples + Number of bananas**
\[ \text{Total fruits} = 3 + 2 + 5 = 10 \]

### Step 2: Identify the number of favorable outcomes for getting an orange or a banana.
- The favorable outcomes for getting an orange = 3 (since there are 3 oranges).
- The favorable outcomes for getting a banana = 5 (since there are 5 bananas).

**Total favorable outcomes for getting an orange or a banana = Number of oranges + Number of bananas**
\[ \text{Favorable outcomes} = 3 + 5 = 8 \]

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

In this case, the event is getting an orange or a banana.
\[ P(\text{Orange or Banana}) = \frac{\text{Favorable outcomes}}{\text{Total fruits}} = \frac{8}{10} \]

### Step 4: Simplify the probability.
- We can simplify \(\frac{8}{10}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.
\[ P(\text{Orange or Banana}) = \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \]

### Final Answer:
The probability of getting an orange or a banana is \(\frac{4}{5}\).

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