Math  /  Data & Statistics

QuestionA certain businessman visits various companies, looking for investors for his startup. It is known that the chance that a potential investor will not decide to engage is 35.5%35.5 \%. We assume that the decisions of potential investors are independent. The businessman continues his visits until the third refusal (i.e. until he sees the third person who decides not to invest). Let XX denote the number of companies visited by the investor. Calculate P(X=10)P(X=10).
Round the result to THREE decinnal places.

Studdy Solution
Substitute the values into the formula:
P(X=10)=(10131)(0.355)3(0.645)103 P(X = 10) = \binom{10-1}{3-1} (0.355)^3 (0.645)^{10-3}
P(X=10)=(92)(0.355)3(0.645)7 P(X = 10) = \binom{9}{2} (0.355)^3 (0.645)^7
Calculate the binomial coefficient:
(92)=9×82×1=36 \binom{9}{2} = \frac{9 \times 8}{2 \times 1} = 36
Calculate P(X=10) P(X = 10) :
P(X=10)=36×(0.355)3×(0.645)7 P(X = 10) = 36 \times (0.355)^3 \times (0.645)^7
P(X=10)=36×0.0447×0.0651 P(X = 10) = 36 \times 0.0447 \times 0.0651
P(X=10)=36×0.00291197 P(X = 10) = 36 \times 0.00291197
P(X=10)=0.104791 P(X = 10) = 0.104791
Round the result to three decimal places:
P(X=10)0.105 P(X = 10) \approx 0.105
The probability P(X=10) P(X = 10) is:
0.105 \boxed{0.105}

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