Chapter 5 review

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.

12!/6!⋅6! =924 2/924 =1/462

In a business class there are 13 business majors and 11 non-business majors. 4 students are randomly selected to present a topic. What is the probability that at least 3 of the 4 students selected are business majors? Express your answer as a fraction or a decimal number rounded to four decimal places.

13+11 =24 24 c 4 =10626 13 c 3 ⋅ 11 c 1 ⋅ 13 c 4 ⋅ 11 c 0 =3146 + 715 =3861 3861/10626 =117/322

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

13/52 + 12/52 - 3/52 =11/26

A coin is tossed 2 times. What is the probability that the number of tails obtained will be between 0 and 2 inclusive? Express your answer as a fraction or a decimal number rounded to four decimal places.

2 c 0 + 2 c 1 + 2 c 2 =4 2^2 (2 tosses 2 outcomes) =4 4/4 =1

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 ⋅ 52 c 2 =16 ⋅ 216⋅ 1326 =4582656

A coin is tossed 4 times. What is the probability that the number of tails obtained will be 1? Express your answer as a fraction or a decimal number rounded to four decimal places.

4 c 1 = 4 2^4 =16 4/16 =1/4

A person rolls a standard six-sided die 7 times. In how many ways can he get 2 fives, 4 ones, and 1 two?

7!/2!⋅4!⋅1! =105

A credit card company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1518 customers. The data is summarized in the table below. What is the probability that a customer is female? Express your answer as a fraction or a decimal number rounded to four decimal places.

767/1518

Evaluate 9!/3!6!

84

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

Not mutually exclusive

Customer account "numbers" for a certain company consist of 4 letters followed by 5 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⋅10⋅10⋅10) =26^4⋅10^5 =456976⋅100000 =45697600000 b. 26 P 4 ⋅ 10 P 5 =10850112000

A mail order company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1871 customers. The data is summarized in the table below. What is the probability that a customer lives in a dorm? Express your answer as a fraction or a decimal number rounded to four decimal places.

customers- 1871 dorm- 202 (m140 f62) 202/1871

You are going to play mini golf. A ball machine that contains 21 green golf balls, 18 red golf balls, 23 blue golf balls, and 17 yellow golf balls, randomly gives you your ball. What is the probability that you end up with a blue golf ball? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

n(E)/n(S) =23/21+18+23+17 =23/79

There are 71 students in a nutrition class. The instructor must choose two students at random. What is the probability that a senior Nutrition major and then a sophomore Nutrition major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

nutrition major seniors- 3 nutrition major soph- 4 3/71 ⋅ 4/70 =12/4970 =0.0024

Larissa is ordering nachos at a restaurant, and the server tells her that she can have up to four toppings: ground beef, black beans, refried beans, and sour cream. 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 Larissa gets just refried beans and sour cream? Express your answer as a fraction or a decimal number rounded to four decimal places.

2⋅ 2 ⋅2 ⋅2 =16 1/16 =0.0625

Cory is planting tulips in his garden, and he has 4 purple bulbs and 4 yellow bulbs to plant in one row. What is the probability that he randomly plants the bulbs so that all 4 purple bulbs are next to each other and all 4 yellow bulbs are next to each other? Express your answer as a fraction or a decimal number rounded to four decimal places.

4+4=8 8!/4!⋅4! =70 2/70 =1/35

A bag contains 5 red, 6 orange, and 7 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 15 jellybeans such that the number of red ones is 5, the number of orange ones is 6, and the number of green ones is 4? Express your answer as a fraction or a decimal number rounded to four decimal places.

5+6+7=18 jellybeans 18 C 5 =816 5 c 5⋅6 c 6⋅7 c 4 =1⋅1⋅35 =35 35/816 -0.0429

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

52 c 3 =22100 48 c 3 =17296 1- (17296/22100) =1201/5525 =0.2174

6 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.

52 c 6 =20,358,520 39 c 6 =3,262,623 1 - (3,262,623/20,358,520) =11051/13160

Evaluate the following expression. n C 1

nCr =n!/r!(n−r)! nC1 =n!/1!(n−1)! 1! =1 n