Question

a bicycle manufacturer is studying the reliability of one of its models. the study finds that the probability of a brake defect is 4 percent and the probability of both a brake defect and a chain defect is 1 percent. if the probability of a defect with the brakes or the chain is 6 percent, what is the probability of a chain defect?
1.5 percent
2 percent
2.5 percent
3 percent

Explanation:

Step1: Definir fórmula de probabilidad

Usamos la fórmula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, donde $A$ es el evento defecto de frenos y $B$ es el evento defecto de cadena.

Step2: Asignar valores dados

Sea $P(A) = 0.04$ (probabilidad de defecto de frenos), $P(A\cap B)=0.01$ (probabilidad de defecto de frenos y cadena) y $P(A\cup B)=0.06$ (probabilidad de defecto de frenos o cadena).

Step3: Despejar $P(B)$

Re - escribimos la fórmula como $P(B)=P(A\cup B)-P(A)+P(A\cap B)$.

Step4: Calcular $P(B)$

Sustituimos los valores: $P(B)=0.06 - 0.04+0.01=0.03$ o 3 por ciento.

Answer:

D. 3 percent