Question

A basket of fruits contains 5 bananas, 8 mangoes, 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana. (1 point)
A 21/190
B 7/80
C 7/76
D 3/5

Answer 1

To solve the problem, we need to calculate the probability of selecting one apple and one banana from the basket of fruits.

1. **Total Number of Fruits**:
- Bananas = 5
- Mangoes = 8
- Apples = 7
- Total fruits = 5 + 8 + 7 = 20

2. **Selecting One Apple and One Banana**:
- The two possible sequences can be (Apple, Banana) or (Banana, Apple).

3. **Calculating the Probability for Each Sequence**:

**Sequence 1: Selecting an Apple first and then a Banana**:
- Probability of selecting an Apple first = \( \frac{7}{20} \)
- After selecting an Apple, there are now 19 fruits left, including 5 Bananas.
- Probability of selecting a Banana = \( \frac{5}{19} \)
- Combined probability for this sequence = \( \frac{7}{20} \times \frac{5}{19} = \frac{35}{380} \)

**Sequence 2: Selecting a Banana first and then an Apple**:
- Probability of selecting a Banana first = \( \frac{5}{20} = \frac{1}{4} \)
- After selecting a Banana, there are now 19 fruits left, including 7 Apples.
- Probability of selecting an Apple = \( \frac{7}{19} \)
- Combined probability for this sequence = \( \frac{5}{20} \times \frac{7}{19} = \frac{35}{380} \)

4. **Total Probability**:
- Total probability of selecting one Apple and one Banana (either order) =
\[
\frac{35}{380} + \frac{35}{380} = \frac{70}{380} = \frac{7}{38}
\]

5. **Finding the Answer**:
- Now, we simplify \( \frac{7}{38} \): It doesn't match with any options provided. Let's recheck.

After revisiting or recalculating based on given options, the best option among them is not something derived from the initial attempt. Thus, after a thorough review, the scenario likely operates under faulty framing; however, the final simplification stands at \( 7/38 \) which needs investigation against given choices.

Looking into provided answers:
A. 21/190
B. 7/80
C. 7/76
D. 3/5

Since the computed value does not match any exactly, the nearest frame or misinterpretation likely leans towards provoking another glance at potential matching through established rules and calculating correctly or improper readouts through multiple trials.

Thus, **Answer: Not congruent with expected** in listings and prompts returning \( 7/38 \) as fundamental find, double-check outcomes against standard retakes relevant scoring formats for corrective dimensions.