Chapter 16

The letters of the word SEED are arranged at random. What is the probability that the arrangement begins and ends with E?

In \(3-22,\) evaluate each expression. $$ _{6} P_{5} $$

For the given values of \(r\) and \(n,\) find the number of ordered selections of \(r\) objects from a collection of \(n\) objects with replacement. \(r=3, n=5\)

Write 10 lines of the Pascal Triangle, starting with 1

In \(7-14,\) answers can be rounded to four decimal places. A store estimates that 1 out of every 25 customers is returning or exchanging merchandise. In the last hour, a cashier had 5 customers. What is the probability that exactly 2 of those were making returns or exchanges?

The letters of the word TOMATO are arranged at random. What is the probability that the arrangement begins and ends with T?

In \(3-22,\) evaluate each expression. $$ _{5} P_{2} $$

For the sample space \(\\{\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\\},\) determine how many events are possible.

In \(12-17,\) write the \(n\) th term of each binomial expansion. $$ (x+y)^{15}, n=3 $$

In \(7-14,\) answers can be rounded to four decimal places. Assume that there are an equal number of births in each month so that the probability is \(\frac{1}{12}\) that a person chosen at random was born in May. A group of 20 friends meet monthly and celebrate the birthdays for that month. What is the probability that at the May celebration, exactly two members of the group have May birthdays?

In \(10-13,\) the mean and standard deviation of a normal distribution are given. Find each probability to the nearest hundredth. mean \(=50,\) standard deviation \(=2.5, P(44 \leq x \leq 50)\)

The letters of the word MATHEMATICS are arranged at random. What is the probability that the arrangement begins and ends with M?

In \(3-22,\) evaluate each expression. $$ _{4} C_{3} $$

State whether the events are independent or dependent. Tossing a coin and rolling a die

In \(7-14,\) answers can be rounded to four decimal places. Using a special type of fishing hook, researchered that the hooking mortality rate was approximately 8\(\%\) . That is, of the fish caught and released with this hook, about 8\(\%\) eventually died. A fisherman caught and released 5 fish using this hook. What is the probability that all 5 fish will live?

In \(12-17,\) write the \(n\) th term of each binomial expansion. $$ (x+y)^{10}, n=7 $$

In \(10-13,\) the mean and standard deviation of a normal distribution are given. Find each probability to the nearest hundredth. mean \(=8,\) standard deviation \(=1, P(7 \leq x)\)

The letters of the word STRAWBERRIES are written on cards and the cards are then shuffled. A card is picked at random. Find the probability that the card contains: $$ \begin{array}{ll}{\text { a. the letter } S} & {\text { b. the letter } R} \\\ {\text { c. a consonant }} & {\text { d. a letter in the word CREAM }}\end{array} $$

In \(3-22,\) evaluate each expression. $$ _{12} C_{7} $$

State whether the events are independent or dependent. Selecting a winner and a runner-up from 7 contestants

In \(12-17,\) write the \(n\) th term of each binomial expansion. $$ (2 x+y)^{6}, n=4 $$

In \(7-14,\) answers can be rounded to four decimal places. Statisticians investigating the Internet-surfing habits of students at a large high school discovered that only 35\(\%\) are interested in protecting their privacy online. What is the probability that none of four randomly chosen students are interested in protecting their privacy?

In \(14-17\) , use the normal approximation to estimate each probability. Round your answers to three decimal places. . \(P(\text { at least } 20 \text { successes }), p=\frac{1}{6}, n=100\)

A piggy bank contains 60 pennies, 25 nickels, 10 dimes, and 5 quarters. If it is equally likely that any one of the coins will fall out when the bank is turned upside down, what is the probability that the coin is: $$ \begin{array}{ll}{\text { a. a penny? }} & {\text { b. a dime? }} \\ {\text { c. not a quarter? }} & {\text { d. a nickel or a dime? }}\end{array} $$

In \(3-22,\) evaluate each expression. $$ _{12} C_{5} $$

State whether the events are independent or dependent. Picking 2 cards from a standard deck without replacing the first card

In \(12-17,\) write the \(n\) th term of each binomial expansion. $$ (x-y)^{9}, n=5 $$

In \(14-17\) , use the normal approximation to estimate each probability. Round your answers to three decimal places. . \(P(\text { more than } 20 \text { successes }), p=\frac{1}{10}, n=200\)

In \(3-22,\) evaluate each expression. $$ _{10} P_{4} \div 4 ! $$

State whether the events are independent or dependent. Buying a magazine and a snack for a train trip

In \(12-17,\) write the \(n\) th term of each binomial expansion. $$ (3 a+2 b)^{7}, n=6 $$

In \(14-17\) , use the normal approximation to estimate each probability. Round your answers to three decimal places. . \(P(\text { fewer than } 60 \text { successes }), p=\frac{5}{6}, n=75\)

A coin that was tossed \(1,000\) times came up heads 526 times. Determine the experimental probabilities for heads and tails.

In \(3-22,\) evaluate each expression. $$ \left(\begin{array}{c}{15} \\ {5}\end{array}\right) $$

State whether the events are independent or dependent. Choosing a size and a color for a sweater

In \(12-17,\) write the \(n\) th term of each binomial expansion. $$ \left(y-\frac{1}{y}\right)^{8}, n=4 $$

In \(14-17\) , use the normal approximation to estimate each probability. Round your answers to three decimal places. . \(P(\text { at most } 100 \text { successes }), p=\frac{6}{7}, n=125\)

A die was rolled \(1,200\) times and a 5 came up 429 times. a. Find the experimental probability for rolling a \(5 .\) b. Based on a comparison of the experimental and theoretical probabilities, do you think the die is fair? Explain your answer.

In \(3-22,\) evaluate each expression. $$ \left(\begin{array}{l}{15} \\ {10}\end{array}\right) $$

State whether the events are independent or dependent. Writing a 5-letter word using the alphabet if letters cannot be repeated

The weather report gives the probability of rain on Saturday as 40\(\%\) and the probability of rain on Sunday as 60\(\% .\) What is the probability that it will rain on Saturday but not rain on Sunday?

In \(3-22,\) evaluate each expression. $$ \left(\begin{array}{l}{4} \\ {4}\end{array}\right) $$

Determine the number of possible outcomes. Tossing a die 3 times

In \(18-20,\) for the given expansion, identify which term is shown and write the next term. $$ (5 c-2 d)^{4} ;-160 c d^{3} $$

A variety box of instant oatmeal contains 10 plain, 6 maple, and 4 apple- cinnamon flavored packets. Ernestine reaches in and takes 3 packets without looking. Find each probability: $$ \begin{array}{ll}{\text { a. } P(2 \text { plain })} & {\text { b. } P(1 \text { maple, } 1 \text { apple-cinnamon })} \\ {\text { c } P(2 \text { plain, } 1 \text { maple })} & {\text { d. } P(1 \text { of each flavor) }}\end{array} $$

In \(3-22,\) evaluate each expression. $$ \left(\begin{array}{c}{12} \\ {0}\end{array}\right) $$

Determine the number of possible outcomes. Tossing a coin 5 times

In \(18-20,\) for the given expansion, identify which term is shown and write the next term. $$ \left(\frac{x}{2}-2 y\right)^{11} ; \frac{165}{4} x^{7} y^{4} $$

A landscape company will replace any shrub that they plant if it fails to grow. They estimate that the probability of failure to grow is \(.02 .\) What is the probability that, of the 200 shrubs planted this week, at most 3 must be replaced?

The quality control department of a company that produces flashbulbs finds that 1 out of \(1,000\) bulbs tested fails to function properly. The flashbulbs are sold in packages of four. What is the probability that all the bulbs in a package will function properly?