Question

lucy observed cars passing on a highway for 1 hour and recorded the data shown below. type of vehicle probabilities sports utility sedan pickup truck vehicle 0.29 0.47 0.24 lucy also noted that the probability that a given vehicle is a red pickup truck is 0.06. assuming that vehicle color and vehicle type are independent, what is the probability that a given vehicle is red? clear all 0.0144 0.18 0.3 0.25

Explanation:

Step1: Definir fórmula de probabilidad condicional

Dado que el color y el tipo de vehículo son independientes, $P(A\cap B)=P(A)\times P(B)$. Aquí, $A$ es el evento de que el vehículo sea rojo y $B$ es el evento de que sea un camión pickup. Sabemos que $P(\text{pickup truck}) = 0.24$ y $P(\text{red pickup truck})=0.06$.

Step2: Calcular $P(\text{red})$

Usando la fórmula $P(\text{red}\cap\text{pickup truck})=P(\text{red})\times P(\text{pickup truck})$, despejamos $P(\text{red})$. Entonces $P(\text{red})=\frac{P(\text{red}\cap\text{pickup truck})}{P(\text{pickup truck})}$.
Sustituyendo los valores dados: $P(\text{red})=\frac{0.06}{0.24}$.

Step3: Realizar cálculo

$\frac{0.06}{0.24}= 0.25$

Answer:

0.25