Question

parked in the lot beside a local grocery store are 2 red cars, 9 white cars, 3 black cars, 1 blue car, and 6 brown cars, all belonging to shoppers in the store. assuming the shoppers leave randomly, what is the probability that the first two cars to leave are white? (1 point)

8/49

11/21

9/49

6/35

Explanation:

Step1: Calculate total number of cars

Total cars \(=2 + 9+3 + 1+6=21\)

Step2: Calculate probability of first car being white

Probability of first car white \(P_1=\frac{9}{21}\)

Step3: Calculate probability of second car being white (after one white car has left)

After one white car leaves, there are \(9 - 1 = 8\) white cars and \(21- 1=20\) total cars. Probability \(P_2=\frac{8}{20}\)

Step4: Calculate combined probability

Using multiplication rule for independent - like (dependent in this case, but formula still \(P = P_1\times P_2\)) events. \(P=\frac{9}{21}\times\frac{8}{20}=\frac{9\times8}{21\times20}=\frac{72}{420}=\frac{6}{35}\)

Answer:

\(\frac{6}{35}\)