Calculating Binomial Probabilities

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Questions

• Why do we have to use "combinations of n things taken x at a time" when we calculate binomial probabilities?
• Question #3a8c6
• What defines a binomial distribution?
• What is a binomial distribution?
• What is the difference between binomial distribution and Poisson distribution?
• What is the probability of getting 7 heads and 7 tails with 14 coin flips?
• What is the general formula for the variance and mean of a binomial distribution?
• What is the standard deviation of a binomial distribution with n=10 and p=0.70?
• What is the difference between a normal and binomial distribution?
• What is the variance of a binomial distribution for which n = 75 and p = 0.20?
• Is a binomial distribution supposed to be symmetrical?
• An electrical retailer receives a shipment of DVD players every day. The probability that a shipment contains a defective player is 0.06. What is the probability that only two shipments contain a defective player in a given week?
• For binomial distribution X, with n = 7 and p = 0.6, what is P(X>3)?
• How does the binomial distribution differ from the Poisson distribution?
• Why can a binomial distribution be used to model the results of a coin toss?
• How is a binomial distribution different from a Bernoulli distribution?
• Half of the passengers who travel on a train buy the 'Daily Boom' before boarding. The train is full and each compartment holds 8 passenger. What is the probability that all the passengers in the compartment have bought the 'Daily Boom'?
• For the binomial distribution n = 17 and p = 0.2, is it suitable to use the normal distribution as an approximation?
• How do you find the mean, variance and standard deviation of the binomial distribution with n = 316 and p = 0.72?
• A fair coin is tossed 60 times. Using the normal approximation to the binomial distribution, what is the probability that a head will show between 32 and 36 times inclusive?
• What is the mean of the binomial distribution for which n=20 and p=0.2?
• Three manufacturing plants, say I, II and III, produce 20, 30 and 50 percent of a company’s output respectively. What is the probability that a randomly-chosen item from the company’s warehouse is defective?
• Maura guesses at all 10 questions on a true/false test. How do you find the probability that she got seven correct?
• Maura guesses at all 10 questions on a true/false test. How do you find the probability that she got at least half correct?
• Suppose a college is considering a new placement test, which has 40% of all students taking remedial arithmetic. If 8 randomly chosen students take the placement test, what is the probability that exactly 2 of them will have to take remedial arithmetic?
• Alexis rolls an 8-sided die 24 times. What is the probability a "five" is rolled at least 4 times, but no more than 18 times?
• Two urns are given.The first one contains two white balls and 3 black ones and the second contains one white ball and 4 red ones. What is the probability that the ball drawn from the second urn is red?
• A government's department of transportation reported that in 2009 Airline A led all domestic airlines in on-time arrivals for domestic flights, with a rate of 83.9%. What is the probability that in the next 6 flights, 4 flights will be on time?
• A government's department of transportation reported that in 2009 Airline A led all domestic airlines in on-time arrivals for domestic flights, with a rate of 83.9%. What is the probability that in the next 6 flights, all 6 flights will be on time?
• What is the probability of 4 successes for a binomial experiment consisting of 11 trials with probability 0.4 of success on each trial?
• In a local college, 20% of the math majors are women. Ten math majors are chosen at random. What is the probability that exactly 2 are women?
• In a local college, 20% of the math majors are women. Ten math majors are chosen at random. How do you find the mean and the variance?
• Given a binomial distribution with n = 8 and p = 0.40, what is the probability that the number of successes is larger than the mean?
• If a binomial distribution applies with a sample size of n = 20, what is the probability of 5 successes if the probability of a success is 0.40?
• Given a binomial distribution with n = 8 and p = 0.40, what is the mean?
• In a survey of 1118 people, 732 people said they voted in a recent presidential election. Given that 63% of eligible voters actually did vote, what is the probability that among the 1118 randomly selected voters , at least 732 actually did vote?
• With n = 13 and p = .4, how do you find P(at least 7) using a binomial probability table?
• Assume a binomial probability distribution with #n = 40# and #pi = .55#. What is the probability that #x# is 15 or less?
• Instructor A of statistics passes 90% of his students. Instructor F passes 60% of his students. A student picks a teacher at random. What is the probability that he passes statistics?
• A collection of 22 laptops includes 6 defective laptops. If a sample of 3 laptops is randomly chosen from the collection, what is the probability that at least one laptop in the sample will be defective?
• When #n=20# and #p=.2#, what is #P(X <= 12)#?
• A 10 question multiple choice exam is given and each question has 5 possible answers. A student takes this exam and guesses at every question. What is the probability they get at least 9 questions correct?
• If n=5 and p=0.6, what is the probability that #P(X=2)#?
• What is the variance of a binomial distribution for which n = 75 and π = 0.20?
• Assume that Tom attends randomly with probability 0.55 and that each decision is independent of previous attendance. What is the probability that he attends at least 7 of 10 classes given that he attends at least 2 but not all 10 classes?
• How do you find the probability of no successes when #n# independent Bernoulli trials are carried out with probability of success #p#?
• How do you find the probability of at least one success when #n# independent Bernoulli trials are carried out with probability of success #p#?
• How do you find the probability of at least two successes when #n# independent Bernoulli trials are carried out with probability of success #p#?
• Consider Bernoulli trials with success probability p=1/4. Given that the first four trials result in all failures, what is the conditional probability that the next four trials are all successes?
• Consider Bernoulli trials with success probability p=1/4. What is the probability that the first success occurs in the fourth trial?
• How do you use the binomial probability formula to find the probability of #x# successes given the probability #p# of success on a single trial for #n=5, x=2, p=0.25#?
• How do you use the binomial probability formula to find the probability of #x# successes given the probability #p# of success on a single trial for #n=6, x=4, p=0.75#?
• He probability of rain on any given day is 2/3. What is the probability of at most one day of rain during the next 3 days?
• Assume that a procedure yields a binomial distribution. What is the probability of x successes if n = 64, x = 3, and p = 0.04?
• Half of the passengers who travel to London buy the 'Daily Boom' before boarding the train. The train is full and each compartment holds 8 passenger. What is the probability that exactly three passengers in a compartment have bought the 'Daily Boom'?
• One day your teacher surprised you with a 22-question multiple-choice quiz. Each question has 4 possible answers, only one of which is correct. What is the probability that you will guess at least 1 correctly?
• One day your teacher surprised you with a 22-question multiple-choice quiz. Each question has 4 possible answers, only one of which is correct. What is the probability that you will guess at most 3 correctly?
• A bookstore determines that two-fifths of the people who come into the store make a purchase. What is the probability that of the 54 people who come into the store during a certain hour, less than 14 make a purchase?
• Of the pupils in a school, 30% travel to school by bus. From a sample of 10 pupils chosen at random, what is the probability that more than 8 travel by bus?
• Let the random variable X denote the number of girls in a five-child family. If the probability of a female birth is 0.5, what are the probabilities of having 0, 1, 2, 3, 4, and 5 girls?
• From experience, the manager of Kramer's Book Mart knows that 60% of the people who are browsing in the store will make a purchase. What is the probability that among ten people who are browsing in the store, at least three will make a purchase?
• The probability that a DVD player produced by VCA Television is defective is estimated to be 0.07. A sample of ten players is selected at random. What is the probability that the sample contains no defective units?
• Assuming that engine failures are independent of each other, what is the probability that on a certain transcontinental flight, a six-engine plane will experience exactly one engine failure?
• 65% of men consider themselves knowledgeable soccer fans. If 14 men are randomly selected, what is the probability that exactly 4 of them will consider themselves knowledgeable fans?
• A child mixes ten good and three dead batteries. To find the dead batteries, his father tests them one by one and without replacement. What is the probability that his father finds all three dead batteries at the fifth test?
• What is the probability that if you threw 20 darts, that 8 of them would hit the same area?
• What is #P(x)# for #n=4, x=1, p= .6#?
• What is #P(x)# for #n= 6,x = 3, q=0.7#?
• What is #P(x)# for #n=3. x = 0, p = 0.8 #?
• What is #P(x)# for #n=4, x=2, p=0.4 #?
• What is #P(x)# for #n=6, x=3, q=0.3 #?
• What is #P(x)# for #n=3. x=1, p=0.9#?
• If #x# is a binomial random variable, what is the probability of #x# for #n = 4, x = 1, p = 0.3#?
• Let #X# be a binomial random variable with #p=0.3# and #n=15#. What is #P(X>9)#?
• Let #X# be a binomial random variable with #p=0.3# and #n=15#. What is #P(X=5)#?
• Let #X# be a binomial random variable with #p=0.3# and #n=15#. What is #P(5≤X≤10)#?
• Let #X# be a binomial random variable with #p=0.6# and #n=10#. What is # P(X ≤ 2) #?
• Let #X# be a binomial random variable with #p=0.6# and #n=10#. What is #P(X > 8) #?
• Let #X# be a binomial random variable with #p=0.4# and #n=10#. What is # P(X = 5) #?
• What is the probability of a student guessing randomly on a test and getting at least 8 out of 10 true and false answers correct?
• A packet of vegetable seeds has a germination rate of 96%. What is the probability that exactly 10 of 12 seeds planted will sprout?
• Teresa and Julia are among 10 students who have applied for a trip to Washington, D.C. Two students from the group will be selected at random for the trip. What is the probability that Teresa and Julia will be the 2 students selected?
• A coin is tossed 16 times. What is the probability of obtaining exactly 14 heads?
• "Compute the probability of #x# successes in the #n# independent trials of the experiment" ?