Probability Statistics Questions

[Boy Tisoy]

1. Given S = {x│x is a distinct letter of the word “prism”}. How many valid events of the sample space S can be formed if it contains “s” but does not contain “m”?
2. In how many ways can 6 people be arranged in a round table if a certain 3 persons refuse to follow each other?
3. A shipment of 12 television sets contains 3 defective sets. In how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?
4. A fair die is rolled until a 4 appears. What is the probability that this die must be rolled more than 10 times?
5. Three dice are thrown. What is the probability that the same number appears on exactly two of the dice?
6. While dressing in the dark you select 2 socks from a drawer containing 5 differently colored pairs. What is the probability that your socks match?
7. In the senior year of a high school graduating class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but neither mathematics nor psychology, 10 studied all three subjects, and 8 did not take any of the three. If a student is selected at random, find the probability that
a. a person enrolled in psychology takes all three subjects;
b. a person not taking psychology is taking both history and mathematics.
8. Suppose that 1 male student out of 10 and 1 female student out of 40 are management majors. Suppose that the student population has twice as many males as females. A student is selected at random from this population and is found to be a management major. What is the probability that the student is a male?
9. A real estate agent has 8 master keys to open several new homes. Only 1 master key will open any given house. If 40% of these homes are usually left unlocked, what is the probability that the real estate agent can get into a specific home if the agent selects 3 master keys at random before leaving the office?
10. Employees in a certain firm are given an aptitude test when first employed. Experience has shown that of the 60% who passed the test, 80% of them were good workers. Of the 40% who failed, 70% of them were rated as bad workers. What is the probability that an employee selected at random will be a good worker?
11. A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 4 times, what is the probability of getting
a. exactly 2 tails?
b. at least 3 heads?

 

[MarkFL]

Hello, and welcome to FMH!

You've posted 11 questions all at once, some of them with multiple parts, without showing any effort. We are not a service where you drop off your homework, and then come back later to pick it up all finished without you having to lift a finger.

I would suggest you begin with the first problem, show us what you've tried, and then we can guide you, where you are an active participant in your own education.

 

[pka]

1. Given S = {x│x is a distinct letter of the word “prism”}. How many valid events of the sample space S can be formed if it contains “s” but does not contain “m”?

4. A fair die is rolled until a 4 appears. What is the probability that this die must be rolled more than 10 times?

@Tisoy. Please read and heed MarkFL reply. This is not a homework service.
Here are hints on two questions. To receive you must show some of your own work.
1) Consider the power set \(\displaystyle T=\mathscr{P}(\{p,~r,~i\})\). How many sets are there in \(\displaystyle T~?\)
Now define \(\displaystyle S=\{X\cup\{s\} | X\in T\}\). Explain why that works.

4) If we toss a die until a four appears, let \(\displaystyle F\) be the number of the toss upon which four appears for the first time.
Now \(\displaystyle \mathcal{P}(F=11)=\left(\frac{1}{6}\right)\left(\frac{5}{6}\right)^{10}\). Explain how & why that works.