Math Problem Statement
A small regional carrier accepted 22 reservations for a particular flight with 19 seats. 17 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 43% chance, independently of each other. Hint: Use the binomial distribution with p = 0.43.
(Report answers accurate to 4 decimal places.)
Find the probability that overbooking occurs.
Find the probability that the flight has empty seats.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Formulas
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
P(Overbooking) = 1 - P(X <= 2)
P(Empty Seats) = P(X <= 1)
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12
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