Chapter 12

A die is rolled, Find each probability. \(P(1 \text { or } 6)\)

Find the variance and standard deviation of each set of data to the nearest tenth. $$ \\{12,14,28,19,11,7,10\\} $$

GAMES For Exercises \(30-35\) , use the following information. A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. The top tile in each stack is chosen. Find each probability. \(P(\text { exactly one is a fish })\)

Determine whether the events are independent or dependent. Then find the probability. Jen's purse contains three \(\$ 1\) bills, four \(\$ 5\) bills, and two \(\$ 10\) bills. If she selects three bills in succession, find the probability of selecting a \(\$ 10\) bill, then a \(\$ 5\) bill, and then a \(\$ 1\) bill if the bills are not replaced.

Josh types the five entries in the bibliography of his term paper in random order, forgetting that they should be in alphabetical order by author. What is the probability that he actually typed them in alphabetical order?

How many different arrangements of the letters of the Hawaiian word aloha are possible?

Prove that \(4+7+10+\cdots+(3 n+1)=\frac{n(3 n+5)}{2}\) for all positive integers \(n\).

A set of 250 data values is normally distributed with a mean of 50 and a standard deviation of 5.5 What percent of the data lies between 39 and 61\(?\)

A die is rolled, Find each probability. \(P(\text { prime number })\)

Give a sample set of data with a variance and standard deviation of 0.

A card is drawn from a standard deck of cards. Find each probability. \(P(\text { jack or queen })\)

GAMES For Exercises \(30-35\) , use the following information. A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. The top tile in each stack is chosen. Find each probability. \(P(\text { both are a fish })\)

Determine whether the events are independent or dependent. Then find the probability. What is the probability of getting heads each time if a coin is tossed 5 times?

Describe an event that has a probability of 0 and an event that has a probability of 1.

How many ways can five members of the 100-member United States Senate be chosen to serve on a committee?

Find the indicated term of each expansion. third term of \((x+y)^{8}\)

A set of 250 data values is normally distributed with a mean of 50 and a standard deviation of 5.5 What is the probability that a data value selected at random is greater than 39\(?\)

Simplify each expression. $$ (x-7)(x+9) $$

Find a counterexample for the following statement. The standard deviation of a set of data is always less than the variance.

BINOMIAL DISTRIBUTION For Exercises 34 and \(35,\) use the following information. You can use a TI-83 \(/ 84\) Plus graphing calculator to investigate the graph of a binomial distribution. \(Step 1\) Enter the number of trials in LI. Start with 10 trials. \(Step 2\) Calculate the probability of success for each trial in \(\mathrm{L} 2\) \(Step 3\) Graph the histogram. Use the arrow and ENTER keys to choose \(\mathrm{ON}\) , the histogram, Li as the Xlist, and \(\mathrm{L} 2\) as the frequency. Use the window \([0,10]\) scl: 1 by \([0,0.5]\) scl: 0.1 What type of distribution does the binomial distribution start to resemble as \(n\) increases?

A card is drawn from a standard deck of cards. Find each probability. \(P(\text { ace or heart) }\)

GAMES For Exercises \(30-35\) , use the following information. A certain game has two stacks of 30 tiles with pictures on them. In the first stack of tiles, there are 10 dogs, 4 cats, 5 balls, and 11 horses. In the second stack of tiles, there are 3 flowers, 8 fish, 12 balls, 2 cats, and 5 horses. The top tile in each stack is chosen. Find each probability. \(P(\text { one is a dog and one is a flower) }\)

Determine whether the events are independent or dependent. Then find the probability. When Ramon plays basketball, he makes an average of two out of every three foul shots he takes. What is the probability that he will make the next three foul shots in a row?

Determine whether each probability is theoretical or experimental. Then find the probability. Two dice are rolled. What is the probability that the sum will be 12?

In a multi-state lottery, the player must guess which five of forty-nine white balls numbered from 1 to 49 will be drawn. The order in which the balls are drawn does not matter. The player must also guess which one of forty-two red balls numbered from 1 to 42 will be drawn. How many ways can the player fill out a lottery ticket?

Find the indicated term of each expansion. fifth term of \((2 a-b)^{7}\)

Simplify each expression. $$ \left(4 b^{2}+7\right)^{2} $$

Consider the two sets of data. A = {1, 2, 2, 2, 2, 3, 3, 3, 3, 4}, B = {1, 1, 2, 2, 2, 3, 3, 3, 4, 4} Find the mean, median, variance, and standard deviation of each set of data.

OPEN ENDED Describe a situation for which the \(P(2 \text { or more) can be found by }\) using a binomial expansion.

A card is drawn from a standard deck of cards. Find each probability. \(P(2 \text { or face card })\)

BASEBALL For Exercises \(36-38\) , use the following information. Albert and Paul are on the school baseball team. Albert has a batting average of \(.4,\) and Paul has a batting average of 3 . That means that Albert gets a hit 40\(\%\) of his at bats and Paul gets a hit 30\(\%\) of his times at bat. What is the probability that- both Albert and Paul are able to get hits their first time at bat?

UTILITIES A city water system includes a sequence of 4 pumps as shown below. Water enters the system at point \(A,\) is pumped through the system by pumps at locations \(1,2,3,\) and \(4,\) and exits the system at point \(B .\) If the probability of failure for any one pump is \(\frac{1}{100},\) what is the probability that water will flow all the way through the system from A to \(\mathrm{B} ?\)

Determine whether each probability is theoretical or experimental. Then find the probability. A baseball player has 126 hits in 410 at-bats this season. What is the probability that he gets a hit in his next at-bat?

Hachi-hachi is a Japanese game that uses a deck of Hanafuda cards which is made up of 12 suits, with each suit having four cards. How many 7-card hands can be formed so that 3 are from one suit and 4 are from another?

Edison is located at (9, 3) in the coordinate system on a road map. Kettering is located at (12, 5) on the same map. Each side of a square on the map represents 10 miles. To the nearest mile, what is the distance between Edison and Kettering?

Simplify each expression. $$ (3 q-6)-(q+13)+(-2 q+11) $$

Explain why each experiment is not a binomial experiment. a. rolling a die and recording whether a \(1,2,3,4,5,\) or 6 comes up b. tossing a coin reatedly until it comes up heads c. removing marbles from a bag and recording whether each one is black or white, if no replacement occurs

Use a calculator to evaluate each expression to four decimal places. $$ e^{-4} $$

BASEBALL For Exercises \(36-38\) , use the following information. Albert and Paul are on the school baseball team. Albert has a batting average of \(.4,\) and Paul has a batting average of 3 . That means that Albert gets a hit 40\(\%\) of his at bats and Paul gets a hit 30\(\%\) of his times at bat. What is the probability that- neither Albert nor Paul is able to get a hit their first time at bat?

Suppose a sport fisher has a 35\(\%\) chance of catching a fish that he can keep each time he goes to a spot. What is the probability that he catches a fish the first times he visits the spot but on the fifth visit he does not?

Determine whether each probability is theoretical or experimental. Then find the probability. A hand of 2 cards is dealt from a standard deck of cards. What is the probability that both cards are clubs?

Solve each equation by factoring. \(x^{2}-16=0\)

PREREQUISITE SKILL Find the indicated term of each expression. third term of \((a+b)^{7}\)

Identify the term that does not belong with the other three. Explain your reasoning. mode \(\qquad\) variance \(\qquad\) mean \(\qquad\) median

CHALLENGE Find the probability of exactly \(m\) successes in \(n\) trials of a binomial experiment where the probability of success in a given trial is \(p .\)

Use a calculator to evaluate each expression to four decimal places. $$ e^{3} $$

BASEBALL For Exercises \(36-38\) , use the following information. Albert and Paul are on the school baseball team. Albert has a batting average of \(.4,\) and Paul has a batting average of 3 . That means that Albert gets a hit 40\(\%\) of his at bats and Paul gets a hit 30\(\%\) of his times at bat. What is the probability that- at least one of the two friends is able to get a hit their first time at bat?

Prove that \(C(n, n-r)=C(n, r)\)

Solve each equation by factoring. \(x^{2}-3 x-10=0\)

fourth term of \((c+d)^{8}\)