A study by a reputable research organization found that when presented with prints from the same​ individual, a fingerprint expert will correctly identify the match 94​% of the time. In​ contrast, a novice will correctly identify the match 75​% of the time. Consider a sample of four different pairs of​ fingerprints, where each pair is a match. Complete parts a and b below.
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Part 1
a. What is the probability that an expert will correctly identify the match in all four pairs of​ fingerprints?
The probability is 
  
enter your response here.
​(Type an integer or decimal rounded to four decimal places as​ needed.)

The probability of an expert correctly identifying the match in a single pair of fingerprints is 94%, or \( 0.94 \).

To find the probability that the expert will correctly identify the match in all four pairs, you multiply the probability of each correct identification because these are independent events.

The probability is calculated as:

\[
P(\text{correct in all 4 pairs}) = 0.94 \times 0.94 \times 0.94 \times 0.94 = 0.94^4
\]

Now, let's calculate:

\[
0.94^4 = 0.7787
\]

Thus, the probability that the expert will correctly identify the match in all four pairs of fingerprints is approximately **0.7787**.

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Would you like to explore more about how this probability works or have any questions? Here are 5 related questions for further exploration:

1. What would be the probability if only 3 out of 4 matches were correctly identified by the expert?
2. How does the probability change if the expert's accuracy increases to 96%?
3. What is the probability that a novice will correctly identify all four pairs of matches?
4. What is the chance that exactly 2 out of the 4 pairs are correctly identified by the expert?
5. How do we calculate the overall probability if both an expert and a novice are involved in identification?

**Tip**: For independent events, the combined probability is the product of individual probabilities.

A study by a reputable research organization found that when presented with prints from the same​ individual, a fingerprint expert will correctly identify the match 94​% of the time. In​ contrast, a novice will correctly identify the match 75​% of the time. Consider a sample of four different pairs of​ fingerprints, where each pair is a match. Complete parts a and b below. Part 1: a. What is the probability that an expert will correctly identify the match in all four pairs of​ fingerprints? The probability is _______.​(Type an integer or decimal rounded to four decimal places as​ needed.)

Learn how to calculate the probability that a fingerprint expert will correctly identify the match in all four pairs of fingerprints. This problem explores probability concepts and the multiplication rule for independent events. Suitable for high school students (Grades 9-12).

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