MAT-152 Chapter 4

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a diamond and not a face card? Express your answer as a fraction or a decimal number rounded to four decimal places.

13(diamonds) - 3(diamond face cards) = 10 10/52 = 5/26 ≈ 0.1923

Given that every seventeenth person in line will get a coupon for a free box of popcorn at the movies, what is the probability that you don't get a coupon when you're in line? Enter a fraction or round your answer to 4 decimal places, if necessary.

16/17 ≈ 0.9412

You are going to play mini golf. A ball machine that contains 23 green golf balls, 24 red golf balls, 18 blue golf balls, and 22 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a yellow golf ball? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

23 + 24 + 18 + 22 = 87 22/87 ≈ 0.2529

If a coin is tossed 3 times, and then a standard six-sided die is rolled 2 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

2^3 * 6^2 * 52C2 = 381888

If a coin is tossed 4 times, and then a standard six-sided die is rolled 3 times, and finally a group of two cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?

2^4 * 6^3 * 52C2 16 * 216 * 1326 = 4582656

A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 5 types of drinks to choose from, 4 types of sandwiches, and 2 types of chips. How many different value meal packages are possible?

5 * 4 * 2 = 40

A person rolls a standard six-sided die 6 times. In how many ways can he get 3 fives, 2 ones, and 1 three?

6! / 3! 2! 1! = 60

A value meal package at Ron's Subs consists of a drink, a sandwich, and a bag of chips. There are 6 types of drinks to choose from, 5 types of sandwiches, and 2 types of chips. How many different value meal packages are possible?

6*5*2 = 60

An Australian Shepherd breeder has had three litters of puppies from the same set of parents. The following table shows the results from the three litters. In the next litter, what is the probability of a puppy having spots? Enter a fraction or round your answer to 4 decimal places, if necessary. Number of Puppies Black and White 6 Red and White 5 Black with Spots 8 Red with Spots 4

All puppies = 6 + 5 + 8 + 4 = 23 Having spots = 8 + 4 = 12 Having spots/All puppies 12/23 ≈ 0.5217

A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2047 class attendees. The data is summarized in the table below. Class Type and Member Status of Class Attendees Class Type Member Non-Member Barre 245 205 Boot Camp 186 194 Boxing 193 200 Spinning 272 276 Yoga 176 100 What is the probability that a class attendee is attending a barre class? Enter a fraction or round your answer to 4 decimal places, if necessary.

Barre = 245 + 205 = 450 450/2047 ≈ 0.2198

Sofia is planting trees along her driveway, and she has 5 willows and 5 cypress trees to plant in one row. What is the probability that she randomly plants the trees so that the two types of trees alternate? Express your answer as a fraction or a decimal number rounded to four decimal places.

E = 2 10! / (5!)(5!) = 252 P(E) = n(E)/n(S) 2/252 = 1/126 ≈ 0.0079

Ella is planting trees along her driveway, and she has 6 sycamores and 6 palm trees to plant in one row. What is the probability that she randomly plants the trees so that the two types of trees alternate? Express your answer as a fraction or a decimal number rounded to four decimal places.

E = 2 12! / 6!6! = 924 2/ 924 = 1/462 ≈ 0.0022

The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. What is the probability that the next fish caught is a drum or a sea trout? Enter a fraction or round your answer to 4 decimal places, if necessary. Number of Fish Caught in March Flounder 286 Red Drum 358 Black Drum 186 Bluefish 341 Sea Trout 247

Fish Caught = 286 + 358 + 186 + 341 + 247 = 1418 Drum or Sea Trout = 385 + 186 + 247 = 791 Drum or Sea Trout /Fish Caught 791/1418 ≈ 0.5578

There are 64 students in a statistics class. The instructor must choose two students at random. Students in a Statistics Class Academic Year Statistics majors non-Statistics majors Freshmen 4 8 Sophomores 7 15 Juniors 8 4 Seniors 14 4 What is the probability that a senior Statistics major and then a freshman non-Statistics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

P(E and F) = P(E) * P(E|F) (14/64) * (8/63) = 1/36 ≈ 0.0278

here are 101 students in a physics class. The instructor must choose two students at random. Students in a Physics Class Academic Year Physics majors non-Physics majors Freshmen 17 11 Sophomores 20 9 Juniors 10 15 Seniors 7 12 What is the probability that a junior non-Physics major and then a freshman Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

P(E and F) = P(E) * P(E|F) (15/101) * (17/100) ≈0.0252

Seventeen college graduates are applying for internships at a Wall Street financial institution. Of these applicants, 4 graduated from an Ivy League university, 10 are finance majors, 5 graduated summa cum laude, and 2 graduated summa cum laude from an Ivy League university. If one resume is selected at random for the first interview, what is the probability that the applicant is either an Ivy League graduate or a summa cum laude graduate? Enter a fraction or round your answer to 4 decimal places, if necessary.

P(E or F) = P(E) + P(F) - P(E and F) (4/17) + (5/17) - (2/17) = 7/17 ≈ 0.4118

Nineteen college graduates are applying for internships at a Wall Street financial institution. Of these applicants, 5 graduated from an Ivy League university, 8 are finance majors, 9 graduated summa cum laude, and 4 graduated summa cum laude from an Ivy League university. If one resume is selected at random for the first interview, what is the probability that the applicant is either an Ivy League graduate or a summa cum laude graduate? Enter a fraction or round your answer to 4 decimal places, if necessary.

P(E or F) = P(E) + P(F) - P(E and F) (5/19) + (9/19) - (4/19) ≈ 0.5263

Jill is ordering pizza at a restaurant, and the server tells her that she can have up to four toppings: green peppers, sausage, steak, and mushrooms. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Jill gets just mushrooms? Express your answer as a fraction or a decimal number rounded to four decimal places.

P(E) = n(E)/n(S) n(E) = 1 n(S) = 2*2*2*2 = 2^4 = 16 = 1/16 ≈ 0.0625

When ordering his new office equipment, Joe must choose one of 9 monitors, one of 5 printers, and one of 5 desk chair styles. Joe likes 1 of the monitors, 3 of the printers, and 4 of the desk chairs. If Joe's boss randomly chooses his equipment for him, what is the probability that Joe will like all the boss's choices? Enter a fraction or round your answer to 4 decimal places, if necessary.

P(joe likes) = number of choices joe likes/number of possible choices = 12/225 = 4/75 ≈ 0.0533

When ordering his new office equipment, Joe must choose one of 8 monitors, one of 5 printers, and one of 9 desk chair styles. Joe likes 4 of the monitors, 4 of the printers, and 2 of the desk chairs. If Joe's boss randomly chooses his equipment for him, what is the probability that Joe will like all the boss's choices? Enter a fraction or round your answer to 4 decimal places, if necessary.

P(joe likes) = number of choices joe likes/number of possible choices number of choices = 8*5*9 = 360 number joe likes = 4*4*2 = 32 32/360 = 4/45 ≈ 0.0889

A person rolls a standard six-sided die 7 times. In how many ways can he get 3 fours, 3 sixes, and 1 two?

Special Permutations 7! / (3! * 3! * 1!) = 140

Customer account "numbers" for a certain company consist of 4 letters followed by 2 numbers. a. How many different account numbers are possible if repetitions of letters and digits are allowed? b. How many different account numbers are possible if repetitions of letters and digits are not allowed?

a. 26 *26 * 26 *26 * 10 * 10 26^4 * 10^2 456976 * 100 = 45697600 b. 26P4 * 10P2 358800 * 90 = 32292000

Customer account "numbers" for a certain company consist of 3 letters followed by 4 numbers. a. How many different account numbers are possible if repetitions of letters and digits are allowed? b. How many different account numbers are possible if repetitions of letters and digits are not allowed?

a. 26*26*26*10*10*10*10 26^3 * 10^4 17576 * 10000 = 175760000 b. 26P3 * 10P4 15600 * 5040 = 78624000

Determine whether the following events are mutually exclusive. a. Choosing a student who is a junior or a physics major from a nearby university to participate in a research study. b. Choosing a student who is a junior or a chemistry major from a nearby university to participate in a research study.

a. Not Mutually Exclusive b. Not Mutually Exclusive

A card is drawn from a standard deck of 52 playing cards. What is the probability that the card will be a spade and an ace? Express your answer as a fraction or a decimal number rounded to four decimal places.

ace of spaces = 1 = 1/52 ≈ 0.0192

A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there were 2047 class attendees. The data is summarized in the table below. Class Type and Member Status of Class Attendees Class Type Member Non-Member Barre 200 160 Boot Camp 215 152 Boxing 232 279 Spinning 171 275 Yoga 192 171 What is the probability that a class attendee is attending a yoga class? Enter a fraction or round your answer to 4 decimal places, if necessary.

Yoga (192 + 171) = 363 Yoga/Total = 363/2047 ≈ 0.1773

3 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.

n(S) = 52C3 = 22100 52(cards) - 13(spades) = 39 n(E^C) = 39C3 = 9139 P(E) = 1 - P(E^C) = 1 - [n(E^C)/n(S)] = 1 - (9139/22100) = 997/1700 ≈ 0.5865

4 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.

n(S) = 52C4 = 270725 52(cards) - 13(spades) = 39 39C4 = 82251 1 - (82251/270725) ≈ 0.6962

Evaluate the following expression. 13! / 9!4!

nCr = n! / r!(n-r)! 13C4 = 715

Evaluate the following expression. 6! / 4!2!

nCr = n! / r!(n-r)! 6C4 = 15

Evaluate the following expression. nPn

nPr = n! / (n-r)! nPn = n! / (n-n)! = n! / 0! 0! = 1 n! / 1 = n!