Question

	Black	Red	Blue	Rows Total
Matte Finish	93	71	176	340
Solid Color	80	156	25	261
Column Totals	173	227	201	601

A) What is the probability that that the car is in Solid Color?

B) What is the probability that a car is picked with Blue color AND contains Solid Color?

C) What is the probability a car is Matte Finished, given it was picked from Black color cars?

D) What is the probability that the company produced Solid Cars or had Blue Color?

E) If two cars are picked without replacement, find the probability that the first is Red with Solid Color, and the second is Black with Matte Finish.

Answer 1

Let S = Event that the car is solid in color B = Event that a car is picked with Blue color M = Event that a car is Matte Finished Bl =  Event that a car is picked with Black color R = Event that a car is picked with Red color

A) To find: Probability that that the car is in Solid Color

B) To find: Probability that a car is picked with Blue color AND contains Solid Color

C) To find: Probability a car is Matte Finished, given it was picked from Black color cars

........................(Property of Conditional probability)

D) To find: Probability that the company produced Solid Cars or had Blue Color

................(Addition theorem of probability)

  

  

  

E) To find: Probability that the first is Red with Solid Color, and the second is Black with Matte Finish when drawn without replacement

Firstly, Probability that the first is Red with Solid Color is picked

And, Probability that the second is Black with Matte Finish

........................( Since, the first ball drawn is not replaced, the grand total (denominator) decreases by one)

Hence, Probability that the first is Red with Solid Color, and the second is Black with Matte Finish when drawn without replacement