A box contains apples, oranges and bananas. The probability of selecting an orange is `5/17` and that of g selecting a banana is `8/17`. A fruit is selected at random. Find the probability that selected fruit is an apple.

Options

A. `4/17`
B. `3/17`
C. `5/17`
D. `8/17`

Answer

To find the probability that the selected fruit is an apple, we can use the information given about the probabilities of selecting oranges and bananas.

**Step 1: Understand the total probability.**
The total probability of all possible outcomes (selecting an apple, an orange, or a banana) must equal 1. This can be expressed as:
\[ P(\text{Apple}) + P(\text{Orange}) + P(\text{Banana}) = 1 \]

**Step 2: Substitute the known probabilities.**
From the problem, we know:
- \( P(\text{Orange}) = \frac{5}{17} \)
- \( P(\text{Banana}) = \frac{8}{17} \)

Now, we can substitute these values into the total probability equation:
\[ P(\text{Apple}) + \frac{5}{17} + \frac{8}{17} = 1 \]

**Step 3: Combine the probabilities of orange and banana.**
Add the probabilities of selecting an orange and a banana:
\[ \frac{5}{17} + \frac{8}{17} = \frac{13}{17} \]

**Step 4: Set up the equation to find \( P(\text{Apple}) \).**
Now substitute this sum back into the equation:
\[ P(\text{Apple}) + \frac{13}{17} = 1 \]

**Step 5: Solve for \( P(\text{Apple}) \).**
To find \( P(\text{Apple}) \), subtract \( \frac{13}{17} \) from 1:
\[ P(\text{Apple}) = 1 - \frac{13}{17} \]

**Step 6: Convert 1 to a fraction with a denominator of 17.**
Convert 1 to a fraction:
\[ 1 = \frac{17}{17} \]

Now substitute:
\[ P(\text{Apple}) = \frac{17}{17} - \frac{13}{17} \]

**Step 7: Perform the subtraction.**
Subtract the fractions:
\[ P(\text{Apple}) = \frac{17 - 13}{17} = \frac{4}{17} \]

Thus, the probability that the selected fruit is an apple is:
\[ P(\text{Apple}) = \frac{4}{17} \]

### Final Answer:
The probability that the selected fruit is an apple is \( \frac{4}{17} \).