Using the Binomial Formula to Solve a Basic Word Problem

  • 1.

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

    Answers:

    • 0.243

    • 0.246

    • 0.249

    • 0.223

  • 2.

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

    Answers:

    • 0.001

    • 0.097

    • 0.096

    • 0.965

  • 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?

    Answers:

    • 0.546

    • 0.055

    • 0.056

    • 0.027

  • 4.

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

    Answers:

    • 0.333

    • 0.015

    • 0.156

    • 0.016

  • 5.

    A true-false 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)

    Answers:

    • 0.117

    • 0.171

    • 0.187

    • 0.7

  • 6.

    A true-false 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)

    Answers:

    • It is more likely that all answers are wrong

    • Neither the first nor the second event can occur

    • It is more likely that 5 answers are right

    • Same probability for both events

  • 7.

    A true-false 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)

    Answers:

    • 0.193

    • 0.054

    • 0.625

    • 0.75

  • 8.

    A multiple-choice 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)

    Answers:

    • 0.0008

    • 0.38

    • 0.0003

    • 0.003

  • 9.

    A multiple-choice 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)

    Answers:

    • It is more likely that all answers are wrong

    • It is more likely that exactly 5 answers are correct

    • Both events have the same probabilities

    • The two events can never occur

  • 10.

    If we select 5 cards from the ordinary 52-card 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.

    Answers:

    • 0.011

    • 0

    • 0.109

    • 0.185

  • 11.

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

    Answers:

    • 0.057

    • 0.143

    • 0.076

    • 0.058

  • 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?

    Answers:

    • 0.422

    • 0.083

    • 0.231

    • 0.043

  • 13.

    We remove from an ordinary 52-card 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.

    Answers:

    • 0.033

    • 0.25

    • 0.243

    • 0.197

  • 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?

    Answers:

    • 0.011

    • 0.013

    • 0.8

    • 0.103

  • 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?

    Answers:

    • 0.267

    • 0.27

    • 0.54

    • 0.207

  • 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?

    Answers:

    • 0.000557

    • 0.000006

    • 0.000051

    • 0.000017

  • 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?

    Answers:

    • 0.006

    • 0.020

    • 0.001

    • 0.005

  • 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?

    Answers:

    • 0

    • 0.002

    • 0.6

    • 0.003

  • 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 non-defectives?

    Answers:

    • 0.03

    • 0.168

    • 0.3

    • 0.068

  • 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?

    Answers:

    • 0.033

    • 0.015

    • 0.145

    • 0.10

  • 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.

    Answers:

    • 0.136

    • 0.24

    • 0.15

    • 0.004

  • 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.

    Answers:

    • 0.2

    • 0.04

    • 0.024

    • 0.002

  • 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?

    Answers:

    • 0.273

    • 0.020

    • 1

    • 0

  • 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?

    Answers:

    • 0.004

    • 0.014

    • 0.001

    • 0.024

  • 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.

    Answers:

    • 0.75

    • 0.007

    • 0.264

    • 0.263

  • 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.

    Answers:

    • 0.004

    • 0.125

    • 0.167

    • 0

  • 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?

    Answers:

    • 0.055

    • 0.005

    • 0.006

    • 0.12

  • 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?

    Answers:

    • 0.478

    • 0.01

    • 0.048

    • 0.005

  • 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?

    Answers:

    • 0.45

    • 0.264

    • 0.462

    • 0.266

  • 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?

    Answers:

    • 1

    • 0.67

    • 0.258

    • 0.301

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