a)
[tex]P(C\cap T) = P(C) \cdot P(T|C) = 0.03 \cdot 0.75 = \underline{\underline{0.0225}} \\ \, \\ \, \\ \, \\ P(\overline C\cap T) = P(\overline C) \cdot P(T|\overline C) = (1-0.03) \cdot 0.05 = 0.97 \cdot 0.05 = \underline{\underline{0.0485}}[/tex]
b)
[tex]P(T_{total}) = P(C\cap T) + P(\overline C \cap T) = 0.0225 + 0.0485 = \underline{\underline{0.071}}[/tex]
c)
[tex]P(C|T) = \frac{P(C) \cdot P(T|C)}{P(T_{total})} = \frac{0.0225}{0.071} \approx \underline{\underline{0.317}}[/tex]
d)
Hendelse:
G = "Går over av seg selv"
[tex]P(G) = 0.60 \\ \, \\ P(\overline{G}) = 0.40[/tex]
[tex]{ {10} \choose {8} } \cdot \left(P(G)\right)^8 \cdot \left(P(\overline G)\right)^{10-8} = 45 \cdot (0.60)^8 \cdot (0.40)^2 \approx \underline{\underline{0.068}}[/tex]
a)
[tex]P(1\, premie) = \frac{ { {4} \choose {4} } } { { {9} \choose {4} } } = \frac{1}{126} \approx \underline{\underline{0.00794}}[/tex]
b)
[tex]P(3\, premie) = \frac{ { {4} \choose {3} } \cdot { {9-4} \choose {4-3} } } {{ {9} \choose {4} }} = \frac{{ {4} \choose {3} } \cdot { {5} \choose {1} }}{{ {9} \choose {4} }} = \frac{4\cdot 5}{126} = \frac{20}{126} = \frac{10}{63} \approx \underline{\underline{0.15873}}[/tex]
c)
[tex]P(2\, premie) = \frac{ { {4} \choose {3} } \cdot { {5} \choose {0} } \cdot { {2} \choose {1} }}{{ {9} \choose {4} }} = \frac{4 \cdot 1 \cdot 2}{126} = \frac{4}{63} \approx \underline{\underline{0.06349}}[/tex]
d)
[tex]P(4\, premie) = \frac{ { {4} \choose {2} } \cdot { {5} \choose {1} } \cdot { {2} \choose {1} }}{{ {9} \choose {4} }} +\frac{ { {4} \choose {2} } \cdot { {5} \choose {0} } \cdot { {2} \choose {2} }}{{ {9} \choose {4} }} = \frac{6\cdot 5 \cdot 2 + 6\cdot 1 \cdot 1}{216} = \frac{66}{126} = \frac{11}{21} \approx \underline{\underline{0.52381}}[/tex]
