Final answer:
To calculate the probability that the first student who passed is the 10th or 13th person asked, use the geometric distribution formula for each scenario and add together for 'or' cases. Use the complement for 'neither' cases.
Step-by-step explanation:
The subject in question involves calculating the probability of specific outcomes using the geometric probability distribution model. This type of problem often comes up in topics such as statistics and probability theory at the high school level.
a. P(10)
The probability that the tenth person is the first to pass is calculated by the formula for a geometric distribution:
(1-p)^(n-1) * p
In this case, p = 0.34, and n = 10. So, the calculation would be:
(1-0.34)^(10-1) * 0.34
b. P(13)
Similarly, for the thirteenth person, you would use the same formula with n = 13:
(1-0.34)^(13-1) * 0.34
c. P(10 or 13)
The probability that the first pass occurs at either the 10th or 13th attempt is found by adding the individual probabilities of those two events:
P(10) + P(13)
d. P(Neither 10 nor 13)
To find the probability that the first person to pass is neither the 10th nor 13th person you ask, you would use the complement rule:
1 - (P(10) + P(13))