You have 58 total fruit only 15 are apples if you randomly pull 3 fruit what is the probability none are apples round to 4 decimal places

The problem asks for the probability that none of the three fruits randomly selected from a total of 58 fruits are apples, given that 15 of the fruits are apples.

### Step 1: Total fruits and apples
- Total fruits = 58
- Apples = 15
- Non-apples = \( 58 - 15 = 43 \)

### Step 2: Probability calculation
We want the probability that none of the selected fruits are apples, meaning we need to select 3 fruits from the 43 non-apples.

The total number of ways to select 3 fruits from 58 is given by the combination:
\[
\binom{58}{3} = \frac{58 \times 57 \times 56}{3 \times 2 \times 1} = 31,896
\]

The number of ways to select 3 fruits from the 43 non-apples is:
\[
\binom{43}{3} = \frac{43 \times 42 \times 41}{3 \times 2 \times 1} = 12,341
\]

### Step 3: Probability
The probability is the ratio of favorable outcomes (selecting from non-apples) to total outcomes (selecting from all fruits):
\[
P(\text{none are apples}) = \frac{\binom{43}{3}}{\binom{58}{3}} = \frac{12,341}{31,896} \approx 0.3869
\]

So, the probability that none of the selected fruits are apples is approximately **0.3869** (rounded to 4 decimal places).

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the probability of selecting at least one apple in 3 pulls?
2. How would the probability change if the total number of apples increased to 20?
3. What is the probability of selecting exactly one apple in 3 pulls?
4. What if you selected 5 fruits instead of 3—what is the probability none are apples?
5. How would the probability change if you pulled the fruits without replacement?

**Tip:** Combinatorics often simplify probability problems by focusing on outcomes without requiring long calculations!

Learn how to calculate the probability of randomly selecting 3 fruits from a group of 58 where none are apples, using combinatorics and probability formulas. This detailed solution is suitable for high school students (Grades 10-12).

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