4.3 - 4.4 HW

The complement of​ "at least​ one" is

"none."

Find the probability that when a couple has three children, at least one of them is a girl.

(1/2)^3 = 1/8 1-1/8 =7/8 ANSWER 7/8

no yes positive- 13 40 negative- 35 11

.755

In a certain​ country, the true probability of a baby being a boy is 0.531. Among the next seven randomly selected births in the​ country, what is the probability that at least one of them is a girl?

1 - .531^7= .988

A presidential candidate plans to begin her campaign by visiting the capitals in 4 of 44 states. What is the probability that she selects the route of four specific​ capitals?

1/3258024

A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 44 states. What is the probability that she selects the route of three specific​ capitals?

1/79464

If you know the names of the remaining eight students in the spelling​ bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling​ bee?

1x2x3x4x5x6x7x8= 40320

If radio station call letters must begin with either K or W and must include either two or three additional​ letters, how many different possibilities are​ there?

2×26×26+2×26×26x26 2×26×26×(1+26) 2×26×26×27=36,504 possibilities

A Social Security number consists of nine digits in a particular​ order, and repetition of digits is allowed. After seeing the last four digits printed on a​ receipt, if you randomly select the other​ digits, what is the probability of getting the correct Social Security number of the person who was given the​ receipt?

4 numbers are known 101010*10= 100000probability is 1/100000

In an​ experiment, college students were given either four quarters or a​ $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts​ (a) through​ (c) below. Students Given Four Quarters purchased: 29 kept: 12 Students Given a​ $1 Bill purchased: 19 kept: 33 A. Find the probability of randomly selecting a student who spent the​ money, given that the student was given a​ $1 bill. B. Find the probability of randomly selecting a student who kept the​ money, given that the student was given a​ $1 bill. C. What do the preceding results​ suggest?

A. 19/52 = .365 B. 33/52= .635 C. A student given a​ $1 bill is more likely to have kept the money.

In an​ experiment, college students were given either four quarters or a​ $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts​ (a) through​ (c) below. Students Given Four Quarters purchased: 29 kept: 18 Students Given a​ $1 Bill purchased: 15 kept: 27 a. Find the probability of randomly selecting a student who spent the​ money, given that the student was given four quarters. b. Find the probability of randomly selecting a student who kept the​ money, given that the student was given four quarters. c. What do the preceding results​ suggest?

A. 29/47 = .617 B. 18/47 = .383 C. A student given four quarters is more likely to have spent the money

The conditional probability of B given A can be found by​ _______.

assuming that event A has​ occurred, and then calculating the probability that event B will occur

A​ _______ probability of an event is a probability obtained with knowledge that some other event has already occurred.

conditional

A thief steals an ATM card and must randomly guess the correct five -digit pin code from a 5-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first​ try?

number of possible codes is 5x5x5x5x5 = 3125 probability that the correct code is given on the first try is 1/3125

purchased kept given 4 quarters 34 13 students given $1

probability .723 .339 .339

In a small private​ school, 6 students are randomly selected from 15 available students. What is the probability that they are the six youngest​ students?

probability 1/5005

The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested negative ​, given that he or she did not have the disease. The individual actually had the disease Positive yes: 130 no: 13 Negative Yes: 16 NO: 141

probability : 141/154= .916

The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test​ result, given that the subject has the disease. What would be an unfavorable consequence of this​ error?The individual actually had the disease Yes no Positive 323 2 Negative 11 1196

probability: 11/334 =.033 The subject would not receive treatment and could spread the disease.

In an​ experiment, college students were given either four quarters or a​ $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts​ (a) through​ (c) below. Students Given Four Quarters purchased: 33 kept: 13 Students Given a​ $1 Bill Purchased: 18 kept: 34 a. Find the probability of randomly selecting a student who spent the​ money, given that the student was given four quarters. b. Find the probability of randomly selecting a student who spent the​ money, given that the student was given a​ $1 bill. c. What do the preceding results​ suggest?

A. 33/46= .717 B. 9/26= .346 C. A student given four quarters is more likely to have spent the money than a student given a​ $1 bill.

Which of the following is NOT a requirement of the Permutations​ Rule, n P r= n!/ (n - r) ! ​, for items that are all​ different?

Order is not taken into account​ (rearrangements of the same items are considered to be the​ same).

Which of the following is NOT a requirement of the Combinations​ Rule, n C r = n !/ r ! ( n - r ) ! ​, for items that are all​ different?

That order is taken into account​ (consider rearrangements of the same items to be different​ sequences).

A classic counting problem is to determine the number of different ways that the letters of "occurrence" can be arranged. Find that number.

The number of different ways that the letters of "occurrence" can be arranged is 151200

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected​ (with replacement). Find the probability that for one such phone​ number, the last four digits include at least one 0

The probability is . 344

How many ways can you make change for a​ quarter? (Different arrangements of the same coins are not counted​ separately.)

Using only​ pennies, nickels, and​ dimes, there are 12 ways to make change for a quarter.