# ~Probability ~

1.A movie rating company classifies movies as good, average, or poor. Movies which are rated by this company fall into these three groups in the proportions 20%, 50%, and 30%, respectively. Base on historical data, the probability a “good” movie will become a blockbuster is 0.7, the probability a “medium” movie will become a blockbuster is 0.5, and the probability a “poor” movie will become a blockbuster is 0.1. The company is now rating the movie “Ironman 4”

(a) Present the above information with a tree diagram.

(b) According to the movie rating company, what is the probability that

“Ironman 4” is a blockbuster?

(c) Given that “Ironman 4” is a blockbuster, what is the probability that it is an

average movie?

2.A computer company finds that the time taken to complete a backup job has a normal distribution with mean 50 minutes and standard deviation 10 minutes.

(a) What percentage of jobs takes less than 35 minutes to finish?

(b) What is the probability that the time taken to complete a backup job is

between 35 minutes and 60 minutes?

(c) Find the time t such that 10% of the backup job has a longer duration than t.

### 1 個解答

• 最佳解答

(1b)

the required probability

= 20% x 0.7 + 50% x 0.5 + 30% x 0.1

= 0.42

(1c)

P(average | blockbuster)

= P(average and blockbuster) / P(blockbuster)

= 50% x 0.5 / 0.42

= 25 / 42

(2)

0.15% 35 2.35% 40 13.5% 45 34% 50 34% 55 13.5% 60 2.35% 65 0.15%

(a) 0.15%

(b) 2.35% + 13.5% + 34% + 34% + 13.5% = 97.35%