36 University » 3 Types of Probability Items to Expect on the ACT ... - Free Printable

To find the probability, we need to determine two things:
1. The total number of possible outcomes: This is the total number of pieces you could possibly pick.
2. The number of favorable outcomes: This is the number of "extra" pieces, since we want to know the chance of picking one of those.

Step 1: Calculate the total number of pieces.
The puzzle box contains the standard 750 pieces plus 5 extra pieces.
$$ \text{Total pieces} = 750 + 5 = 755 $$

So, there are 755 pieces in total that you could pick from.

Step 2: Identify the number of favorable outcomes.
We want to pick one of the extra pieces. There are 5 extra pieces in the box.
$$ \text{Number of extra pieces} = 5 $$

Step 3: Calculate the probability.
Probability is calculated as:
$$ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} $$

Substituting our numbers:
$$ \text{Probability} = \frac{5}{755} $$

Now, let's look at the options provided:
A. $\frac{1}{5}$
B. $\frac{1}{755}$
C. $\frac{1}{750}$
D. $\frac{5}{755}$
E. $\frac{5}{780}$

Our calculated probability is $\frac{5}{755}$, which matches Option D exactly.

*(Note: While you can simplify the fraction $\frac{5}{755}$ to $\frac{1}{151}$ by dividing the top and bottom by 5, the unsimplified version is listed directly as an option, so no further simplification is needed for the final answer.)*

Final Answer:
D