Question 1185737: The following data represents the information on the ratings of a random sample of 152 movies that were released last year and are classified by their genre.
Ratings
Genre PG PG-13 R Total
Action 2 15 17 34
Comedy 16 11 18 45
Drama 7 16 20 43
Thriller20 6 4 30
Total 45 48 59 152
(a) What is the probability that the movie is a thriller and it is rated R?
(b) What is the probability that the movies is either a comedy or it is rated PG-13?
(c) Given that the movie is an action movie, what is the probability that it is rated as PG?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's the breakdown of how to calculate the probabilities:
**(a) Probability of a careless driver under 25:**
* Number of accidents caused by careless drivers under 25: 89
* Total number of accidents: 944
* Probability = (Number of careless drivers under 25) / (Total accidents) = 89 / 944 ≈ 0.0943 (Your provided answer of 0.5667 is incorrect.)
**(b) Probability of drinking and driving OR speeding:**
* Number of accidents caused by drinking and driving: 340
* Number of accidents caused by speeding: 296
* Total accidents: 944
* Probability = (Drinking and driving + Speeding) / Total = (340 + 296) / 944 = 636 / 944 ≈ 0.6737
**(c) Probability of drinking and driving OR a driver under 25:**
* Number of accidents caused by drinking and driving: 340
* Number of accidents involving drivers under 25: 535
* Number of accidents caused by drinking and driving *and* a driver under 25: 286
* Probability = (Drinking and driving + Under 25 - Both) / Total = (340 + 535 - 286) / 944 = 589 / 944 ≈ 0.6239
**(d) Probability the driver was at least 25 GIVEN speeding:**
* Number of accidents caused by speeding: 296
* Number of accidents caused by speeding and a driver 25 or above: 136
* Probability = (Speeding and 25 or above) / (Total speeding) = 136 / 296 ≈ 0.4595
**(e) Probability of two careless driving accidents (without replacement):**
* Probability of the first accident being caused by careless driving: 308 / 944
* After one accident is chosen, there are 943 accidents left, and 307 are caused by careless driving.
* Probability of the second accident being caused by careless driving: 307 / 943
* Probability of both being caused by careless driving = (308 / 944) * (307 / 943) ≈ 0.1066
|
|
|
