Question

1. lucy observed cars passing on a highway for 1 hour and recorded the data shown below.

vehicle probabilities
pickup truck	0.24
sedan	0.47
sports utility vehicle	0.29

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?
0.0144
0.18
0.25
0.30
clear all

Explanation:

Step1: Recall the independence formula

If two events $A$ and $B$ are independent, $P(A\cap B)=P(A)\times P(B)$. Let $A$ be the event that a vehicle is red and $B$ be the event that a vehicle is a pickup - truck. We know $P(B) = 0.24$ and $P(A\cap B)=0.06$.

Step2: Solve for $P(A)$

From $P(A\cap B)=P(A)\times P(B)$, we can rewrite it as $P(A)=\frac{P(A\cap B)}{P(B)}$. Substitute $P(A\cap B) = 0.06$ and $P(B)=0.24$ into the formula: $P(A)=\frac{0.06}{0.24}$.

Step3: Calculate the probability

$\frac{0.06}{0.24}=\frac{6}{24}=0.25$.

Answer:

0.25