Question

1. A standard six-sided die is rolled. What is the probability of rolling a number greater than 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Answer: ____________________

2. A box contains 48 red marbles, 53 white marbles, and 67 blue marbles. If a marble is randomly selected from the box, what is the probability that it is blue? Express your answer as a simplified fraction or a decimal rounded to four decimal places. Answer: ____________________

3. Write out the sample space for the given experiment. Use the following letters to indicate each choice: O for orange, Y for yellow, B for blue, M for maple, E for ebony, and U for unfinished. While renovating your house, you have a choice of paint colors for your game room: orange, yellow, or blue. You also have the following options for the finish on your entertainment center: maple, ebony, or unfinished. Answer: ____________________

4. A box contains 19 large marbles and 11 small marbles. Each marble is either green or white. 5 of the large marbles are green, and 6 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is large or green? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: ____________________

5. A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 9? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: ____________________

6. A newspaper company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1870 customers. The data is summarized in the table below. Gender and Residence of Customers Residence Males Females Apartment 113 227 Dorm 129 254 With Parent(s) 52 165 Sorority/Fraternity House 166 219 Other 262 283 What is the probability that a customer is male and lives in a dorm? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: ____________________

7. Find the number of outcomes in the complement of the given event. Out of 339 raspberry plants in a field, 182 are ready for picking. Answer: ____________________

8. Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a spade, the second card will be a red card, and the third card will be an ace? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: ____________________

9. Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a black card for the second card drawn, if the first card, drawn without replacement, was a club? Express your answer as a fraction or a decimal number rounded to four decimal places. Answer: ____________________

10. Out of 400 applicants for a job, 179 are female and 72 are female and have a graduate degree.

Step 1. What is the probability that a randomly chosen applicant has a graduate degree, given that they are female? Express your answer as a fraction or a decimal rounded to four decimal places. Answer: ____________________

Step 2. If 118 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is female, given that the applicant has a graduate degree? Express your answer as a fraction or a decimal rounded to four decimal places. Answer: ____________________

Answer 1

1.

Sample space, S={1,2,3,4,5,6}; A=event of rolling a number greater than 3={4,5,6}.

Required probability=P(A)=3/6=1/2.

2.

A box contains 48 red marbles+53 white marbles+ 67 blue marbles=168 marbles in total.

If a marble is randomly selected from the box, the probability that it is blue=67/168=0.3988

3. Sample space={(O,M),(O,E),(O,U),(Y,M),(Y,E),(Y,U),(B,M),(B,E),(B,U)}

4. P(large)=19/30, P(green)=(5+(11-6))/30=10/30, P(large and green)=5/30

P(large or green)=P(large)+P(green)-P(large and green)=19/30+10/30-5/30=4/5

5. A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 9? Express your answer as a fraction or a decimal number rounded to four decimal places.

S={(1,1),...,(1,6),(2,1),...,(2,6),...,(6,1),....,(6,6)}

A=event of rolling a sum greater than or equal to 9={(3,6),(4,5),(5,4),(6,3),(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}

P(A)=10/36= 0.2778