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 74% of the time. Consider a sample of six different pairs of fingerprints, where each pair is a match. Complete parts a and b below.

a. What is the probability that an expert will correctly identify the match in all seven pairs of fingerprints?
b. What is the probability that an novice will correctly identify the match in all seven pairs of fingerprints?

a. 0.6899

b. 0.1642

Step-by-step explanation:

a. Given the probability of success is 0.94 for an expert and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of  the events is calculated as:

Hence, the probability of correctly identifying the 6 matches is 0.6899

b.Given the probability of success is 0.74 for a novice and that the number of pairs, n=6:

-Each attempt is independent and therefore the probability of  the events is calculated as:

#Hence, the probability of correctly identifying the 6 matches is 0.1642

*I have used the sample size of 6(due to conflicting info/question size).

There was 443 student tickets sold

Step-by-step explanation:

Step 1:  Make a system of equation

4s + 6n = 4310

s + n = 866

Step 2:  Solve for s to get n

s = 866 - n

4(866 - n) + 6n = 4310

3464 - 4n + 6n - 3464 = 4310 - 3464

2n / 2 = 846 / 2

n = 423

Step 3:  866 - 423 gives us the amount of tickets bought by students

s = 866 - 423

s = 443

 There was 443 student tickets sold