Binomial Probability

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Show your work for each problem.

1.
Which of the following is a requirement for a binomial experiment?
1. a)Outcomes can vary each trial
2. b)At least 100 trials required
3. c)Probability changes between trials
4. d)Trials must be independent
2.
What is ?
3.
In the formula , what does represent?
1. a)Number of trials
2. b)Number of successes
3. c)Probability of success on each trial
4. d)Probability of failure
4.
If , what is ?
5.
A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads?
6.
Calculate .
7.
Which scenario is NOT a binomial experiment?
1. a)Rolling a die 6 times and counting sixes
2. b)Testing if 8 light bulbs work
3. c)Flipping a coin 10 times
4. d)Drawing 5 cards from a deck without replacement
8.
A basketball player makes 60% of free throws. What is the probability of making exactly 3 out of 5 free throws?
9.
What is ? Round to 4 decimal places.
10.
In a binomial experiment with and , which value of has the highest probability?
1. a)
2. b)
3. c)
4. d)
11.
A multiple choice test has 8 questions with 4 options each. If you guess randomly, what is the probability of getting exactly 2 correct?
12.
Calculate .
13.
A drug has an 80% success rate. If 6 patients take it, what is the probability that ALL 6 respond positively?
1. a)
2. b)
3. c)
4. d)
14.
A quality inspector finds defects in 5% of products. In a sample of 10 products, what is the probability of finding exactly 1 defect?
15.
What is the probability of getting NO successes in 4 trials if ? Round to 4 decimal places.
16.
What is ?
1. a)1
2. b)0
3. c)Undefined
4. d)5
17.
What is ?
18.
A vaccine is 90% effective. In a group of 7 vaccinated people, what is the probability that exactly 6 are protected?