Math 10 Practice Exam 1 and Math 10 Exam 1 question

(NOTE ANSWER NEED TO BE CORRECT AND PLS SHOW WORK---- NO EXCEPTION)

Question 1

Five cards are drawn from a deck of 52 cards without replacement. Find the probability that three of the cards drawn are not diamonds. A.)0.0815

B.) 0.2509

C.) 0.9185

D.) 0.0660

E.) 0.2743

Question 2

A regular six-sided die is rolled 1000 times. Use the binomial distribution to determine the standard deviation for the number of times an odd number is rolled. A.) 15.8

B.) 22.4

C.) 250

D.) 26.6

E.) 500

Question 3

What is the probability of getting all tails in three tosses of a fair coin?

A.) 0.0625

B.) 0.5

C.) 0.25

D.) 0.03125

E.) 0.125

Question 4

A random variable X has a mean of 1127 and a standard deviation of 13. By Chebyshev's theorem, the probability that X will be between 1075 and 1179 is at least

A.) 88.9%

B.) 93.75%

C.) 96%

D.) 75%

E.) 80%

Question 5

A certain toxin is lethal in 1% of cases. If 15 cases are selected at random, what is the probability that the toxin was lethal in at least one case?

A.) 14%

B.) 1.5%

C.) 15%

D.) 1%

E.) 0.15%

Question 6

A person pays $5 to draw a card. If a heart or a diamond is drawn, the player wins $1. If a club is drawn, the player wins $5. If a spade is drawn, the player wins $10. What is the expected value of this game?

A.) -$1.25

B.) -$0.50

C.) -$4.25

D.) -$0.25

E.) -$0.75

Question 7

A pair of dice is rolled. Find the probability of rolling "snake eyes" (i.e., rolling a sum of two) given that a sum less than 6 is rolled.

A.) 7%

B.) 15%

C.) 10%

D.) 13%

E.) 5%

Question 8

Use the binomial distribution to determine the expected number of jacks drawn in 1000 draws with replacement from a deck of 52 cards. Round your answer to the nearest whole number. A.) 115

B.) 154

C.) 77

D.) 19

E.) 38

Question 9

The number of computer related work orders filed in a given day has the following probability distribution. Find the standard deviation of X.

X	0	1	2	3	4	5
P(X)	0.44	0.31	0.16	0.05	0.03	0.01

A.) 1.11

B.) 0.95

C.) 1.23

D.) 2.13

E.) 1.46

Question 10

A pair of dice is rolled. What is the probability of rolling a sum of 5, 7, or 11?

A.) 0.300

B.) 0.083

C.) 0.250

D.) 0.306

E.) 0.333

Question 11

A school of 55 artists has 30 painters and 25 sculptors. A panel of 14 artists is randomly selected from the school. Find the probability that the panel consists of 6 painters and 8 sculptors.

A.) 0.174

B.) 0.153

C.) 0.161

D.) 0.125

E.) 0.148

Question 12

How many distinct arrangements of the letters in the word "sleeveless" are possible?

A.) 302,400

B.) 12,600

C.) 151,200

D.) 25,200

E.) 3,628,800

Question 13

A recent poll found that 42% of those surveyed like the new mayor. If 5 people are selected at random, what is the probability that all 5 don't like the new mayor?

A.) 0.987

B.) 0.580

C.) 0.013

D.) 0.066

E.) 0.934

Question 14

How many four-character alpha-numeric codes are possible if repeated characters are allowed?

A.) 1,679,616

B.) 456,976

C.) 358,800

D.) 58,905

E.) 1,413,720

Question 15

The table below summarizes the results of a pharmaceutical drug study.

	Drug is effective	Drug is ineffective
Symptoms are acute	47	76
Symptoms are not acute	89	54

A study participant is randomly selected. What is the probability the participant's symptoms are acute given that the drug is ineffective?

A.) 0.462

B.) 0.585

C.) 0.489

D.) 0.618

E.) 0.286

Question 16

A sample of 4 different keyboards is randomly selected from a stockroom containing 11 that are defective and 27 that have no defects. What is the probability that at least one of the keyboards is defective?

A.) 0.745

B.) 0.238

C.) 0.110

D.) 0.781

E.) 0.762

Question 17

The table below shows the coding scheme preferences of 280 urgent care centers.

	Region 1	Region 2	Region 3
Coding scheme A	40	25	30
Coding scheme B	35	45	20
Coding scheme C	20	30	35

If one of the 280 care centers is randomly selected, find the probability that the center uses coding scheme B or is located in region 1.

A.) 0.696

B.) 0.357

C.) 0.339

D.) 0.571

E.) 0.538

Question 18

Use the binomial distribution to find the probability of getting five spades in ten draws with replacement from a standard deck of 52 playing cards.

A.) 12.4%

B.) 10.9%

C.) 5.8%

D.) 7.6%

E.) 25%

Question 19

There are 27 Bertie Bott's Every Flavour Beans in a bowl, of which 9 are red, 10 are orange, and 8 are blue. You randomly select one bean, eat it, and then select a second bean. Find the probability that the first bean is blue and the second is red.

A.) 64/729

B.) 8/81

C.) 4/351

D.) 2/19

E.) 4/39

Question 20

The number of computer related work orders filed in a given day has the following probability distribution. Find the mean of X.

X	0	1	2	3	4	5
P(X)	0.44	0.31	0.16	0.05	0.03	0.01

A.) 1.23

B.) 2.13

C.) 1.46

D.) 1.11

E.) 0.95