
1.
If we toss a fair coin 9 times, what is the probability of getting exactly 5 heads?

2.
A fair coin is tossed 10 times. What is the probability of getting all tails?

3.
In 8 tosses of a fair coin, what is the probability of getting exactly 2 heads with one of the heads on the first toss?

4.
A fair coin is tossed 6 times. What is the probability of obtaining no tails?

5.
A truefalse test consists of 10 questions. If a student guesses every answer, what is the probability that he will score exactly 70%? (Students receive equally weighted points for each correct answer)

6.
A truefalse test consists of 10 questions. If a student guesses every answer, which is more likely: to answer all questions incorrectly, or to answer 5 questions correctly? (Students receive equally weighted points for each correct answer)

7.
A truefalse test consists of 12 questions. What is the probability that a student gets exactly 75%, just by guessing? (Students receive equally weighted points for each correct answer)

8.
A multiplechoice test consists of 10 questions, each with 4 choices (only one choice is correct). What is the probability of getting an 80% , by guessing? (Students receive equally weighted points for each correct answer)

9.
A multiplechoice test consists of 10 questions, each with 4 choices (only one choice is correct). If a student guesses at each question, which is more likely: that all her answers are wrong, or that exactly 5 answers are correct? (Students receive equally weighted points for each correct answer)

10.
If we select 5 cards from the ordinary 52card deck with replacement (the drawn card is replaced in the deck after each trial), what is the probability of getting exactly 4 picture cards?
Note: Pictures cards are the Jack, Queen, and King.

11.
We select 7 card from the ordinary 52card deck with replacement (the drawn card is replaced in the deck after each trial). What is the probability of obtaining exactly 4 spades?

12.
We combine together two ordinary card decks and select with replacement 3 cards (the drawn card is replaced in the deck after each trial). What is the probability of selecting exactly one club card?

13.
We remove from an ordinary 52card deck all picture cards. Then, we choose 3 cards with replacement (the drawn card is replaced in the deck after each trial). What is the probability of getting exactly an 8?
Note: Pictures cards are the Jack, Queen, and King.

14.
In a college, 80% of the students support their city's football team. What is the probability that in a random sample of 15 students exactly 10 of them will support the team?

15.
In a small city, 54% of the electorate voted for the mayor. What is the probability that in a sample of 8 voters, exactly 4 have voted for the mayor?

16.
A manufacturing process produces, on the average, 25 defective items out of 1000. If we select 6 items randomly, what is the probability of getting exactly 4 defectives?

17.
A pharmaceutical company produces sleeping pills that are shipped internationally. The pills cause serious excessive sleepiness in 2% of the patients. In a sample of 20 patients, what is the probability that exactly 4 of them have suffered from oversleeping?

18.
A manufacturing process produces, on the average, 30% defective items. If the quality control manager selects 5 items randomly, what is the probability that all the items will be defectives?

19.
A manufacturing process produces, on the average, 30% defective items. If one of the managers selects 5 items randomly, what is the probability that all the items will be nondefectives?

20.
A supermarket has assigned only one of its several cash registers to an express lane which serves customers who have purchased less than 8 items in total. The probability that a customer in this supermarket will use the express lane is 10%. If we select 6 customers, what is the probability that there are exactly 3 who will use the express lane?

21.
In a survey of the employees of a large company, 30% of all employees anonymously said that they were dissatisfied at work. Find the probability that among 8 randomly selected employees who were surveyed exactly 4 were dissatisfied with working condition.

22.
60% of all families in an American neighborhood possess more than 2 cars. If 15 families are randomly chosen, find the probability that exactly 5 of them possess more than 2 cars.

23.
2% of an exceptionally large number of parcels shipped by a renowned mailing service company were erroneously mailed with incorrect postage. What is the probability that in a randomly selected sample of 100 parcels exactly 2 were erroneously mailed with incorrect postage?

24.
In a town of 15,000,000 people there are 600,000 mathematicians. If we randomly choose 5 people in this town, what is the probability that exactly 2 of them are mathematicians?

25.
If 9 in 12 customers at an American shopping mall arrive by automobile, find the probability that 3 of 5 customers will arrive by automobile.

26.
If 9 in 12 customers at a European shopping mall arrive by automobile, find the probability that 1 of 6 customers will arrive by automobile.

27.
A medical doctor knows from experience that 5 in 25 patients are late for their appointment. What is the probability that 6 of 10 patients are late for their appointment?

28.
A pharmaceutical company claims that one of its drugs causes serious side effects in 1 person out of 200, on the average. To check the validity of the claim, a physician administers this drug to 10 randomly chosen patients and finds out that exactly 1 of them suffers from serious side effects. If the company's claim is correct , how probable is it to obtain the physician's result?

29.
In a large shipment of tomatoes, 75% are green and therefore nor ready for sale to customers. What is the probability that 3 of 5 tomatoes randomly chosen are green and so not ready for sale to the customers?

30.
The principal of a college claims that 67% of the college's students are admitted in some of the 10 renowned universities of their country. If his claim is correct, what is the probability that in a sample of 3 of his students all of them will study in one of the 10 universities of the country?