There is 45 total fruit only 13 are apples if you randomly select 4 fruit what is the probability at least one is an apple

To calculate the probability that at least one of the four randomly selected fruits is an apple, we'll use the complement rule. Instead of directly calculating the probability of selecting at least one apple, it's easier to first find the probability of selecting **no apples** and subtract that from 1.

### Step 1: Find the probability of selecting **no apples**.

- There are 45 total fruits, and 13 of them are apples.
- The remaining fruits that are **not apples** is \( 45 - 13 = 32 \).

When randomly selecting 4 fruits without replacement, the probability that none of the selected fruits are apples can be calculated by considering the probability of selecting 4 fruits from the 32 that are not apples.

The probability of selecting no apples is:
\[
P(\text{no apples}) = \frac{32}{45} \times \frac{31}{44} \times \frac{30}{43} \times \frac{29}{42}
\]

### Step 2: Calculate \( P(\text{no apples}) \).

\[
P(\text{no apples}) = \frac{32}{45} \times \frac{31}{44} \times \frac{30}{43} \times \frac{29}{42}
\approx 0.5276
\]

### Step 3: Find the probability of **at least one apple**.

The probability of selecting at least one apple is the complement of selecting no apples:
\[
P(\text{at least one apple}) = 1 - P(\text{no apples})
\]
\[
P(\text{at least one apple}) = 1 - 0.5276 = 0.4724
\]

Thus, the probability of selecting at least one apple is approximately **0.4724** or **47.24%**.

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Would you like further details or clarification on this solution? 

Here are 5 related questions to explore further:

1. What is the probability of selecting exactly one apple from the 4 fruits?
2. How would the probability change if you were selecting 5 fruits instead of 4?
3. What is the probability that all 4 selected fruits are apples?
4. How would the probability change if there were 50 fruits instead of 45, with 13 still being apples?
5. How can the binomial probability formula be applied in this context?

**Tip**: When solving probability problems, identifying the complement (what you don't want) can often make the calculation easier!

Explore how to calculate the probability of selecting at least one apple when randomly choosing 4 fruits from a total of 45 fruits, with 13 apples. This problem covers important probability concepts and applies the complement rule for a clear solution. Suitable for students in Grades 10-12.

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