43. Se sabe que el 70% de los miembros de la universidad son fumadores;[br]en una muestra aleatoria de 18 fumadores, ¿Cuál es la probabilidad de que haya[br]exactamente 16 fumadores?[br][br][br][color=#ff0000]Datos:[br][/color][br]p=70% = 0,7 probabilidad de que sean fumadores.[br][br]q=30%=0,3 probabilidad de que no sean fumadores.[br][br]X=16[br][br]n=18 muestra[br][br][color=#ff0000]DESARROLLO DEL EJERCICIO[br][img]data:image/png;base64,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[/img][br][br][br][math]\text{P(16)= \frac{18!}{16!\:\left(18-16\right)!}.(0,7)^{16}.(0,3)^{18-16}}[/math][br][math]\text{P(16)=\frac{18!}{16!\:\left(2\right)!}.(0,7)^{16}.(0,3)^2}[/math][br][math]\text{P(16)=\frac{18.17.16!}{16!\:\left(2\right)} .(0,7)^{16}.(0,3)^2}[/math][br][math]\text{P(16)=\frac{18.17}{2}.(0,7)^{16}.(0,3)^2}[/math][br][math]\text{P(16)=0,04576=4,58\varkappa}[/math][br][br][br][/color][br][br][br]