Math Problem Statement
This problem follows a binomial distribution with ( n = 17 ) properties and a success probability ( p = 0.3 ). We want the probability of selling more than 4 properties, which is ( P(X > 4) ).
First, calculate ( P(X \leq 4) ) using the binomial probability formula:
[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} ]
Then subtract from 1 to find ( P(X > 4) ). This requires calculating ( P(X = 0) ) through ( P(X = 4) ):
- ( P(X = 0) )
- ( P(X = 1) )
- ( P(X = 2) )
- ( P(X = 3) )
- ( P(X = 4) )
Summing these and subtracting from 1:
[ P(X > 4) = 1 - \sum_{k=0}^{4} P(X = k) ]
Computing this, we find:
[ P(X > 4) \approx 0.7477 ]
Thus, the probability is approximately 0.7477.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Cumulative Probability
Formulas
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
P(X > 4) = 1 - P(X \leq 4)
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12
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