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)Probability changes between trials
2. b)At least 100 trials required
3. c)Trials must be independent
4. d)Outcomes can vary each trial
2.
What is $\binom{4}{2}$ ?
3.
In the formula $P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}$ , what does $p$ represent?
1. a)Probability of success on each trial
2. b)Number of successes
3. c)Number of trials
4. d)Probability of failure
4.
If $p = 0.3$ , what is $1-p$ ?
5.
A fair coin is flipped 4 times. What is the probability of getting exactly 2 heads?
6.
Calculate $\binom{6}{3}$ .
7.
Which scenario is NOT a binomial experiment?
1. a)Testing if 8 light bulbs work
2. b)Drawing 5 cards from a deck without replacement
3. c)Rolling a die 6 times and counting sixes
4. d)Flipping a coin 10 times
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 $(0.7)^4$ ? Round to 4 decimal places.
10.
In a binomial experiment with $n=8$ and $p=0.5$ , which value of $k$ has the highest probability?
1. a) $k = 0$
2. b) $k = 8$
3. c) $k = 4$
4. d) $k = 2$
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 $\binom{10}{4}$ .
13.
A drug has an 80% success rate. If 6 patients take it, what is the probability that ALL 6 respond positively?
1. a) $\binom{6}{5}(0.8)^5(0.2) \approx 0.393$
2. b) $(0.8)^6 \approx 0.262$
3. c) $(0.2)^6 \approx 0.000064$
4. d) $6 \times 0.8 = 4.8$
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 $p = 0.3$ ? Round to 4 decimal places.
16.
What is $\binom{5}{0}$ ?
1. a)0
2. b)5
3. c)Undefined
4. d)1
17.
What is $\binom{7}{7}$ ?
18.
A vaccine is 90% effective. In a group of 7 vaccinated people, what is the probability that exactly 6 are protected?