# 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?

• 0.243

• 0.246

• 0.249

• 0.223

• 2.

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

• 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?

• 0.546

• 0.055

• 0.056

• 0.027

• 4.

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

• 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)

• 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)

• 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)

• 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)

• 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)

• 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.

• 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?

• 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?

• 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.

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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?

• 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.

• 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.

• 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?

• 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?

• 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.

• 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.

• 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?

• 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?

• 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?

• 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?