Question

kira was on the internet researching prices of new and used cars. one website has 15 cars for sale, 4 of which were sedans and 7 of which were trucks. if kira randomly chose to look at 4 of the cars in a specific order, what is the probability that the first 2 cars are sedans and the last 2 are trucks? write your answer as a decimal rounded to four decimal places.

Explanation:

Step1: Calculate probability of first sedan

The probability that the first - car is a sedan is $\frac{4}{15}$ since there are 4 sedans out of 15 cars.

Step2: Calculate probability of second sedan

After choosing one sedan, there are 3 sedans left out of 14 cars. So the probability that the second car is a sedan is $\frac{3}{14}$.

Step3: Calculate probability of first truck

After choosing 2 sedans, there are 7 trucks out of 13 cars. So the probability that the third car is a truck is $\frac{7}{13}$.

Step4: Calculate probability of second truck

After choosing 2 sedans and 1 truck, there are 6 trucks left out of 12 cars. So the probability that the fourth car is a truck is $\frac{6}{12}$.

Step5: Calculate the overall probability

The overall probability is the product of the probabilities of each step. $P=\frac{4}{15}\times\frac{3}{14}\times\frac{7}{13}\times\frac{6}{12}$.
$P=\frac{4\times3\times7\times6}{15\times14\times13\times12}=\frac{504}{32760}\approx0.0154$.

Answer:

0.0154