Question

a study found that 23% of the cars manufactured last year were suvs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white suvs. to the nearest whole percent, what is the probability that a car is an suv, given that it is white? 9% 15% 21% 57%

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Let $A$ be the event that a car is an SUV and $B$ be the event that a car is white.

Step2: Identify the given probabilities

We are given that $P(A) = 0.23$, $P(B)=0.13$, and $P(A\cap B)=0.02$.

Step3: Calculate the conditional probability

Substitute the values into the formula: $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0.02}{0.13}\approx 0.1538$.

Step4: Convert to percentage

Multiply the result by 100 to get the percentage: $0.1538\times100 = 15.38\%$. Rounding to the nearest whole - percent gives $15\%$.

Answer:

15%