Question 1

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.
-In how many ways can the men be presented first and then the women?

Accepted Answer

A)   72
B)   144
C)   5,040
D)   2 B

Question 2

Find the probability.
-A card is drawn at random from a standard 52-card deck. Find the probability that the card is Neither an ace nor a heart.

Accepted Answer

A)    413\frac { 4 } { 13 }134​ 
B)    913\frac { 9 } { 13 }139​ 
C)    2126\frac { 21 } { 26 }2621​ 
D)    3552\frac { 35 } { 52 }5235​ B

Question 3

Solve the problem.
-Three noncollinear points determine a triangle. How many triangles can be formed with 8 points, No three of which are collinear?

Accepted Answer

A)   6720
B)   24
C)   336
D)   56 D

Question 4

Evaluate the expression.
-$${ } _ { 7 } \mathrm { C } _ { 4 }$$

Accepted Answer

A)   420
B)   210
C)   35
D)   12

Question 5

Find the probability.
-In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 Physics majors is chosen. Find the probability that exactly 4 are not ethnic minorities. Round to The nearest ten-thousandth.

Accepted Answer

A)   0.2564
B)   0.2253
C)   0.0547
D)   0.0467

Question 6

Find the indicated probability.
-If $P ( A ) = 0.4 , P ( B ) = 0.5$, and $P ( A$ and $B ) = 0.3$, find $P ( A$ or $B )$.

Accepted Answer

A)    P(A\mathrm { P } ( \mathrm { A }P(A  or  
B)  =0.8\mathrm { B } )  = 0.8
B)  =0.8 
B)    P(A\mathrm { P } ( \mathrm { A }P(A  or  
B)  =0.5\mathrm { B } )  = 0.5
B)  =0.5 
C)    P(A\mathrm { P } ( \mathrm { A }P(A  or  
B)  =0.6\mathrm { B } )  = 0.6
B)  =0.6 
D)    P(A\mathrm { P } ( \mathrm { A }P(A  or  
B)  =0.9\mathrm { B } )  = 0.9
B)  =0.9

Question 7

Find the probability.
-A 10-question multiple choice test has 4 possible answers for each question. A student selects at Least 6 correct answers. Round to the nearest thousandth.

Accepted Answer

A)   0.020
B)   0.118
C)   0.989
D)   0.995

Question 8

Find the probability.
-The distribution of B.A. degrees conferred by a local college is listed below, by major. $$\begin{array} { l | c } 
\text { Major } & \text { Number of Students } \
\hline \text { English } & 2073 \
\text { Mathematics } & 2164 \
\text { Chemistry } & 318 \
\text { Physics } & 856 \
\text { Liberal Arts } & 1358 \
\text { Business } & 1676 \
\text { Engineering } & 868 \
\text { Total: } & 9313
\end{array}$$ What is the probability that a randomly selected degree is not in Mathematics? Round to the Nearest thousandth.

Accepted Answer

A)   0.768
B)   0.682
C)   0.303
D)   0.232

Question 9

Solve the problem.
-A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find The probability that the family has no boys.

Accepted Answer

A)    116\frac { 1 } { 16 }161​ 
B)    120\frac { 1 } { 20 }201​ 
C)    18\frac { 1 } { 8 }81​ 
D)    1516\frac { 15 } { 16 }1615​

Question 10

Solve the problem.
-Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your Number comes up, you get $600.00. Find the expected winnings.

Accepted Answer

A)   -$0.42
B)   -$0.40
C)   -$0.50
D)   -$1.00

Question 11

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability.
-The second marble is red given the first marble is white.

Accepted Answer

A)    332\frac { 3 } { 32 }323​ 
B)    328\frac { 3 } { 28 }283​ 
C)    27\frac { 2 } { 7 }72​ 
D)    14\frac { 1 } { 4 }41​

Question 12

Solve the problem.
-An insurance company says that at age 50 one must choose to take $10,000 at age 60, $30,000 at 70, Or $50,000 at 80 ($0 death benefit). The probability of living from 50 to 60 is 0.87, from 50 to 70, 0.62, and from 50 to 80, 0.42. Find the expected value at each age.

Accepted Answer

A)    60:$8700 60: \$ 8700 60:$8700  70:$12,600 70: \$ 12,600 70:$12,600  80:$21,000 80: \$ 21,000 80:$21,000  
B)    60:$6200 60: \$ 6200 60:$6200  70:$18,600 70: \$ 18,600 70:$18,600  80:$21,000 80: \$ 21,000 80:$21,000 
C)   60:  $8700 \$ 8700 $8700 70:  $18,600 \$ 18,600 $18,600 80: \$21,000
D)   60:  $8700 \$ 8700 $8700  70:$26,100 70: \$ 26,100 70:$26,100 80:  $43,500 \$ 43,500 $43,500

Question 13

Find the probability
-You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing Cards. Find the probability that both cards are black.

Accepted Answer

A)    1351\frac { 13 } { 51 }5113​ 
B)    2551\frac { 25 } { 51 }5125​ 
C)    25102\frac { 25 } { 102 }10225​ 
D)    12652\frac { 1 } { 2652 }26521​

Question 14

Solve the problem.
-A contractor is considering a sale that promises a profit of $26,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $1000 with a probability of 0.3. What is the expected Profit?

Accepted Answer

A)   $18,200
B)   $25,000
C)   $18,900
D)   $17,900

Question 15

Solve the problem.
-One card is selected from a deck of cards. Find the probability of selecting a black card or a jack.

Accepted Answer

A)    1526\frac { 15 } { 26 }2615​ 
B)    2752\frac { 27 } { 52 }5227​ 
C)    126\frac { 1 } { 26 }261​ 
D)    713\frac { 7 } { 13 }137​

Question 16

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.
-In how many ways can the people be presented?

Accepted Answer

A)   5,040
B)   2,520
C)   49
D)   720

Question 17

Solve the problem.
-If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a ʺdoubleʺ.

Accepted Answer

A)    16\frac { 1 } { 6 }61​ 
B)    13\frac { 1 } { 3 }31​ 
C)    15\frac { 1 } { 5 }51​ 
D)    14\frac { 1 } { 4 }41​

Question 18

Find the probability
-In one town, 32% of all voters are Democrats. If two voters are randomly selected for a survey, find The probability that they are both Democrats. Round to the nearest thousandth.

Accepted Answer

A)   0.320
B)   0.102
C)   0.099
D)   0.640

Question 19

Solve the problem.
-Use a tree diagram showing all possible results when four fair coins are tossed to list the ways of Getting more than two tails.

Accepted Answer

A)   hhtt, htht, htth, httt, thht, thth, thtt, tthh, ttht, ttth, tttt
B)   hhtt, htht, htth, thht, thth, tthh
C)   httt, thtt, ttht, ttth, tttt
D)   httt, thtt, ttht, ttth

Question 20

Use the counting principle to obtain the answer.
-A restaurant offered salads with 3 types of lettuce, 3 different toppings, and 6 different dressings. How many different types of salad could be offered?

Accepted Answer

A)   12
B)   36
C)   27
D)   54

Exam 11: Probability

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. -In how many ways can the men be presented first and then the women?

Find the probability. -A card is drawn at random from a standard 52-card deck. Find the probability that the card is Neither an ace nor a heart.

Solve the problem. -Three noncollinear points determine a triangle. How many triangles can be formed with 8 points, No three of which are collinear?

Evaluate the expression. - ${ } _ { 7 } \mathrm { C } _ { 4 }$

Find the probability. -In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 Physics majors is chosen. Find the probability that exactly 4 are not ethnic minorities. Round to The nearest ten-thousandth.

Find the indicated probability. -If $P ( A ) = 0.4 , P ( B ) = 0.5$ , and $P ( A$ and $B ) = 0.3$ , find $P ( A$ or $B )$ .

Find the probability. -A 10-question multiple choice test has 4 possible answers for each question. A student selects at Least 6 correct answers. Round to the nearest thousandth.

Solve the problem. -A couple plans to have four children. Using a tree diagram , obtain the sample space. Then, find The probability that the family has no boys.

Solve the problem. -Numbers is a game where you bet $1.00 on any three-digit number from 000 to 999. If your Number comes up, you get $600.00. Find the expected winnings.

Two marbles are drawn without replacement from a box with 3 white, 2 green, 2 red, and 1 blue marble. Find the probability. -The second marble is red given the first marble is white.

Solve the problem. -An insurance company says that at age 50 one must choose to take $10,000 at age 60, $30,000 at 70, Or $50,000 at 80 ($0 death benefit) . The probability of living from 50 to 60 is 0.87, from 50 to 70, 0.62, and from 50 to 80, 0.42. Find the expected value at each age.

Find the probability -You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing Cards. Find the probability that both cards are black.

Solve the problem. -A contractor is considering a sale that promises a profit of $26,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $1000 with a probability of 0.3. What is the expected Profit?

Solve the problem. -One card is selected from a deck of cards. Find the probability of selecting a black card or a jack.

An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. -In how many ways can the people be presented?

Solve the problem. -If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a ʺdoubleʺ.

Find the probability -In one town, 32% of all voters are Democrats. If two voters are randomly selected for a survey, find The probability that they are both Democrats. Round to the nearest thousandth.

Solve the problem. -Use a tree diagram showing all possible results when four fair coins are tossed to list the ways of Getting more than two tails.

Use the counting principle to obtain the answer. -A restaurant offered salads with 3 types of lettuce, 3 different toppings, and 6 different dressings. How many different types of salad could be offered?