Vocab
In your own words, what does probability mean?
The likelihood that some event occurs.
A spinner can land on either red, blue, or green. You spin once.
What is the sample space of this event?
A fair coin is flipped 20 times. You count the number of heads.
Is this binomial? Why?
Yes, it meets all of the requirements
A fair coin is flipped 10 times. What is the probability of getting exactly 6 heads?
0.205
20.5%
A fair coin is flipped 12 times. What is the probability of getting at most 4 heads?
0.194
19.4%
A basketball player makes 80% of their free throws. They take 25 shots. Let X be the number of made shots.
Find the n, and p values, and find the mean.
n: 25
p: 0.8
Mean: 20
What is the formula for the mean of a binomial distribution?
np
1/2
A jar contains 8 red and 12 blue marbles. You draw 5 marbles without replacement and count how many are red.
Is this binomial? Why?
No, probability changes
A basketball player makes free throws with probability 0.8. In 8 attempts, what is the probability of making exactly 5 shots?
0.147
14.7%
A basketball player makes free throws with probability 0.75. In 10 attempts, what is the probability of making at least 8 shots?
0.526
52.6%
A factory produces light bulbs with a 10% defect rate. A sample of 50 bulbs is inspected. Let X be the number of defective bulbs.
Find the standard deviation.
SD: 2.12
What are the four requirements for a binomial distribution?
1. Only two options
2. Set number of trials
3. Independent events
4. Same probability of success
A bag contains 8 red balls and 12 blue balls. If one ball is drawn at random, what is the complement of the event "drawing a red ball"?
Drawing a blue ball
An online quiz randomly selects 10 questions from a large question bank, where each question has a 0.8 probability of being answered correctly. You count the number of correct answers.
Is it binomial? Why?
Yes, it meets all the requirements.
A factory has a 10% defect rate. If 12 items are inspected, what is the probability exactly 2 are defective?
0.23
23%
A factory produces items with a 5% defect rate. If 20 items are inspected, what is the probability of no more than 2 defects?
0.925
92.5%
A multiple-choice test has questions where a student guesses randomly with a 25% chance of getting each correct. There are 20 questions. Let X be the number of correct answers.
Find the mean, variance, and standard deviation.
Mean: 5
Variance: 3.75
SD: 1.94
What is the formula for the variance of a binomial distribution?
npq
1/13
A machine produces bolts, and historically, 2% are defective. A quality inspector checks bolts until 3 defective ones are found and records the number of bolts inspected.
Is it binomial? Why?
No, not a fixed amount of trials
A multiple-choice test has 5 questions, each with 4 choices. A student guesses randomly. What is the probability they get exactly 3 correct?
0.88
8.8%
A student has a 0.6 probability of answering each question correctly. On a 15-question test, what is the probability of getting at least 10 correct?
0.403
40.3%
A fair coin is flipped 40 times. Let X be the number of heads.
Find the mean, variance, and standard deviation.
Mean: 20
Variance: 10
SD: 3.16
What is the formula for the standard deviation of a binomial distribution?
sqrt(npq)
Find the probability of NOT rolling a number greater than 4 on a die.
2/3
A survey is conducted by calling people at random until 50 people agree to participate. You record how many calls were made.
Is it binomial? Why?
No, not a fixed amount of trials.
A new medication works for 70% of patients. If 6 patients take it, what is the probability exactly 4 respond positively?
0.324
32.4%
A survey shows 30% of people prefer a product. If 8 people are selected, what is the probability that fewer than 3 prefer it?
0.552
55.2%
A new medication is effective for 65% of patients. If 30 patients take the medication, let X be the number of patients for whom it is effective.
Mean: 19.5
Variance: 6.825
SD: 2.61