Free Printable Binomial Probability Requirements

1.

Evaluate $_8C_5$

a)

336

b)

56

c)

8/5

d)

40,320

2.

Which descriptions are true for a binomial distribution?

a)

the probability of success must be the same for each event

b)

the probability for each event must be 0.5

c)

there can be only two possible outcomes

d)

The probabilities must add to 1

e)

each trial must be independent

3.

A fair coin is tossed 100 times. What is the probability that:

a. heads will appear exactly 55 times?

a)

4.85 %

b)

9.18 %

c)

86.4 %

d)

18.4 %

4.

In a certain town, 75% of all drivers are insured. What is the expected number of insured drivers present in a group of 200 randomly selected townspeople?

a)

75

b)

150

c)

175

d)

125

5.

In a certain town, 90% of the people drive without ever looking at their phones. In a group of 200 randomly selected citizens, what is the variance?

a)

18

b)

4.24

c)

180

d)

90

6.

At a certain restaurant, there is a 70% probability that the flowers on your table will be yellow. If you are there with a group that is occupying 6 tables, what is the probability that 5 of the tables will have yellow flowers?

a)

70%

b)

70.6 %

c)

30.3 %

d)

5.0 %

7.

If you are randomly selecting a day, the probability of selecting a Saturday is 1/7. If 10 days are randomly selected, what is the standard deviation?

a)

1.22

b)

1

c)

1/7

d)

1.11

8.

Which of the following could be examples of binomial probabilities? (select all that apply)

a)

P(success)=0.99, P(failure) = 0.01

b)

P(A) = 0.4, P(B) = 0.4

c)

P(A)= 1/3, P(B) = 1/3, P(C) = 1/3

d)

P(3)= 1/6, P(not 3) = 5/6

9.

Evaluate $_9C_6$

a)

54

b)

504

c)

60,480

d)

84

10.

It is believed that 33% of adults HAVE NEVER read a book since graduating from high school.

If you randomly selected 500 post-high school adults, How many of them would you expect to find in that group who HAD read a book since high school?

a)

335

b)

33

c)

165

d)

67

11.

A fair coin is tossed 100 times. What is the probability that:

b. there will be at most 55 heads?

a)

4.85 %

b)

9.18 %

c)

86.44 %

d)

18.4 %

12.

A fair coin is tossed 100 times. What is the probability that:

c. there will be at least 55 heads?

a)

4.85 %

b)

9.18 %

c)

86.4 %

d)

18.41 %

13.

A fair coin is tossed 100 times. What is the probability formula to find that:

a. heads will appear exactly 48 times?

(Check all that apply)

a)

$\left(_{100}C_{48}\right)\left(0.5\right)^{48}\left(1-0.5\right)^{52}$

b)

$\left(_{100}C_{48}\right)\left(0.5\right)^{52}\left(1-0.5\right)^{48}$

c)

$binompdf\left(100,0.5,48\right)$

d)

$\left(_{100}C_{48}\right)\left(0.5\right)^{48}\left(0.5\right)^{52}$

14.

At a certain restaurant, there is a 70% probability that the flowers on your table will be yellow. If you are there with a group that is occupying 6 tables, what is the probability that at most 5 of the tables will have yellow flowers?

a)

70%

b)

88.2 %

c)

30.3 %

d)

42 %

15.

At a certain restaurant, there is a 70% probability that the flowers on your table will be yellow. If you are there with a group that is occupying 6 tables, what is the probability that at least 5 of the tables will have yellow flowers?

a)

70%

b)

88.2 %

c)

30.3 %

d)

42 %

16.

At a certain restaurant, there is a 70% probability that the flowers on your table will be yellow. If you are there with a group that is occupying 6 tables, what is formula to find the probability that at most 5 of the tables will have yellow flowers?

(Check all that apply)

a)

$\left(_6C_5\right)\left(0.70\right)^5\left(1-0.70\right)^1$

b)

$binomcdf\left(6,0.70,5\right)$

c)

$binompdf\left(6,0.70,5\right)$

d)

\left(_6C_5\right)\left(0.70\right)^5\left(0.30\right)^{ }

17.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening? Is this a binomial setting?

a)

Yes. All "BINS" conditions are met

b)

No. The independent condition is not satisfied because we are sampling without replacement.

18.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening?

Find the probability of getting 5 green Skittles if this is not a binomial setting. Think P(1st green AND 2nd green AND 3rd green ….). Show your work.

P(All 5 green) = P(G and G and G and G and G)

P(All green) = (2000/10000) * (1999/9999) * (1998/9998) * (1997/9997) * (1996/9996) = ???

Use a calculator to find your answer. Express your answer to the nearest hundred thousandths.

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19.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening?

Find the probability of getting 5 green Skittles if this were a binomial setting. Think binomial formula. Show your work.

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20.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening?

How do your answers from #18 and #19 compare? Why do you think this is?

a)

The answer of #18 and #19 are almost the same. The probabilities in #18 change so little because sample is small relative to population. Check the 10% condition.

n\le0.10\left(N\right)

5\le0.10\left(10000\right)

5\le1000

Therefore, the 10% solution is satisfied. This can be considered in a binomial setting.

b)

pick the other choice as your answer.

21.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening?

Mr. Wilcox now grabs a huge handful of 100 Skittles from the large bin of 10,000 Skittles. Let X = number of green Skittles in a handful of 100 Skittles. X can be considered a binomial random variable because the 10% condition is satisfied.

What is the probability of getting at most 11 green Skittles? Show work

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22.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening?

Mr. Wilcox now grabs a huge handful of 100 Skittles from the large bin of 10,000 Skittles. Let X = number of green Skittles in a handful of 100 Skittles. X can be considered a binomial random variable because the 10% condition is satisfied.

With n = 100, p = 0.20, X=11, Refer to the online binomial calculator to draw the graph of the binomial distribution.

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23.

In 2013 Skittles changed the flavor of green from lime to sour apple (big mistake!!). Dr. Salva takes a small handful of 5 Skittles from a bin of 10,000 Skittles and gets ALL GREEN (terrible)! If 20% of the Skittles are green, what is the probability of this happening?

Mr. Wilcox now grabs a huge handful of 100 Skittles from the large bin of 10,000 Skittles. Let X = number of green Skittles in a handful of 100 Skittles. X can be considered a binomial random variable because the 10% condition is satisfied.

With n = 100, p = 0.20, X=11, Calculate the mean and standard deviation of X.

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Binomial Probability Requirements

Total questions: 23

Worksheet time: 1hrs 11mins

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