Se tienen dos bolsas, una con bolillas rojas numeradas del 1 al 5 y la otra con bolillas amarillas?

Hola.

Veamos como construimos el espacio muestral

Primera urna<img src="https://tex.z-dn.net/?f=U_1%3D%5C%7B1%2C2%2C3%2C4%2C5%5C%7D" />

Segunda urna<img src="https://tex.z-dn.net/?f=U_2%3D%5C%7B1%2C2%2C3%2C4%2C5%2C6%2C7%5C%7D" />

a)El espacio muestral<img src="https://tex.z-dn.net/?f=%5COmega%3DU_1%5Ctimes%20U_2" /> es decir

<img src="https://tex.z-dn.net/?f=%5COmega%3D%5C%7B%281%2C1%29%2C%281%2C2%29%2C%281%2C3%29%2C%281%2C4%29%2C%281%2C5%29%2C%281%2C6%29%2C%281%2C7%29%2C%5C%5C%20%0A%5Chspace%2A%7B0.9cm%7D%282%2C1%29%2C%282%2C2%29%2C%282%2C3%29%2C%282%2C4%29%2C%282%2C5%29%2C%282%2C6%29%2C%282%2C7%29%2C%5C%5C%0A%5Chspace%2A%7B0.9cm%7D%283%2C1%29%2C%283%2C2%29%2C%283%2C3%29%2C%283%2C4%29%2C%283%2C5%29%2C%283%2C6%29%2C%283%2C7%29%2C%5C%5C%0A%5Chspace%2A%7B0.9cm%7D%284%2C1%29%2C%284%2C2%29%2C%284%2C3%29%2C%284%2C4%29%2C%284%2C5%29%2C%284%2C6%29%2C%284%2C7%29%2C%5C%5C%0A%5Chspace%2A%7B0.9cm%7D%285%2C1%29%2C%285%2C2%29%2C%285%2C3%29%2C%285%2C4%29%2C%285%2C5%29%2C%285%2C6%29%2C%285%2C7%29%0A%5C%7D" />

b) Hallemos la suma de los números implicados en el espacio muestral de cada par ordenado

<img src="https://tex.z-dn.net/?f=%5COmega_%5Csum%3D%5C%7B2%2C3%2C3%2C4%2C4%2C4%2C4%2C5%2C5%2C5%2C5%2C6%2C6%2C6%2C6%2C6%2C7%2C7%2C7%2C7%2C7%2C%5C%5C%0A%5Chspace%2A%7B1.2cm%7D8%2C8%2C8%2C8%2C8%2C9%2C9%2C9%2C9%2C10%2C10%2C10%2C11%2C11%2C12%5C%7D" />

Hay 37 sumas

¿cuántas sumas mayores que 7 hay?

Hay cinco 8's

hay cuatro 9's

hay tres 10's

hay dos 11's

hay un 12

en total hay 15 sumas mayores que 7.

Por lo tanto la probabilidad es 15 / 37

c) si vemos el espacio muestral en (a) tenemos 5 números iguales donde la muestra es 35, por ende la probabilidad de extraer números iguales es 5 / 35 = 1 / 7.