A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow

marble. Two marbles are chosen (without replacement). (a) What is the

probability that one will be green and the other red? (b) What is the probability

that one will be blue and the other yellow?

10. You roll a fair die five times, and you get a 6 each time. What is the probability

that you get a 6 on the next roll?

11. You win a game if you roll a die and get a 2 or a 5. You play this game 60

times.

a. What is the probability that you win between 5 and 10 times (inclusive)?

b. What is the probability that you will win the game at least 15 times?

c. What is the probability that you will win the game at least 40 times?

d. What is the most likely number of wins.

e. What is the probability of obtaining the number of wins in d?

Explain how you got each answer or show your work.

12. In a baseball game, Tommy gets a hit 30% of the time when facing this pitcher.

Joey gets a hit 25% of the time. They are both coming up to bat this inning.

a. What is the probability that Joey or Tommy will get a hit?

b. What is the probability that neither player gets a hit?

c. What is the probability that they both get a hit?

13. An unfair coin has a probability of coming up heads of 0.65. The coin is flipped

50 times. What is the probability it will come up heads 25 or fewer times?

(Give answer to at least 3 decimal places).

14.You draw two cards from a deck, what is the probability that:

a. both of them are face cards (king, queen, or jack)?

b. you draw two cards from a deck and both of them are hearts?

. (a) What is the probability of rolling a pair of dice and obtaining a total score of

9 or more? (b) What is the probability of rolling a pair of dice and obtaining a

total score of 7?

2. A box contains four black pieces of cloth, two striped pieces, and six dotted

pieces. A piece is selected randomly and then placed back in the box. A second

piece is selected randomly. What is the probability that:

a. both pieces are dotted?

b. the first piece is black and the second piece is dotted?

c. one piece is black and one piece is striped?

3. A card is drawn at random from a deck. (a) What is the probability that it is an

ace or a king? (b) What is the probability that it is either a red card or a black

card?

4. The probability that you will win a game is 0.45. (a) If you play the game 80

times, what is the most likely number of wins? (b) What are the mean and

variance of a binomial distribution with p = 0.45 and N = 80?

5. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

6.When Susan and Jessica play a card game, Susan wins 60% of the time. If they

play 9 games, what is the probability that Jessica will have won more games than

Susan?

7.You flip a coin three times. (a) What is the probability of getting heads on only

one of your flips? (b) What is the probability of getting heads on at least one flip?

8. A test correctly identifies a disease in 95% of people who have it. It correctly

identifies no disease in 94% of people who do not have it. In the population, 3%

of the people have the disease. What is the probability that you have the disease

if you tested positive

A college student is taking a Mathematics and a Statistics course. The probability she passes the Mathematics course is 0.8. The probability she passes the Statistics course is 0.6. The probability she passes at least one of the courses is 0.84. Let A and B be the events that she passes the Mathematics course and the Statistics course, respectively. Answer the next four questions. What is the probability she passes both courses? (a) 0.06 (b) 0.18 (c) 0.48 (d) 0.56 (e) 0.68 Answer: 0.56 Given that she passes the Mathematics course, what is the probability that she will pass the Statistics course? (a) 0.93 (b) 0.82 (c) 0.75Question (1) In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the probability that (a) the student take mathematics or history; (b) the student take history but not mathematics; (c) the student does not take history if he took mathematics. Solution:Result Pass Fail Total Mathematics 45 35 80 Course English 12 90 Total 93 77 170 2. (3 points) What is the probability that randomly selected student takes a course in Mathematics and fails? 3. (5 points) What is the probability that randomly selected student either takes a course in Mathematics or fails? 4. (7 points) What is the probability that a randomly selected student takes course in Mathematics given the information that student fails?2. The mean mathematics SAT score in 2015 was 514 with a standard deviation of 11?. Assume the mathematics SAT score is normally distributed. Also draw the normal curves wherever necessary.r a.) State the random variable. (2 Marks) to Find the probability that a person has a mathematics SAT score over 700 (6 Marks) c.) Find the probability that a person has a mathematics SAT score of less than 400. (6 Marks) a; Find the probability that a person has a mathematics SAT score between a 5'30 and a 650 (6 Marks)