Module 5 Problems

  1. A ball is drawn randomly from a jar that contains 6 red balls, 2 white balls, and 5 yellow balls. Find the probability of the given event.
    1. A red ball is drawn
    2. A white ball is drawn
  2. Suppose you write each letter of the alphabet on a different slip of paper and put the slips into a hat. What is the probability of drawing one slip of paper from the hat at random and getting:
    1. A consonant
    2. A vowel
  3. A group of people were asked if they had run a red light in the last year. 150 responded “yes”, and 185 responded “no”. Find the probability that if a person is chosen at random, they have run a red light in the last year.
  4. In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats.
  5. Compute the probability of tossing a six-sided die (with sides numbered 1 through 6) and getting a 5.
  6. Compute the probability of tossing a six-sided die and getting a 7.
  7. Giving a test to a group of students, the grades and gender are summarized below. If one student was chosen at random, find the probability that the student was female.
A B C Total
Male 8 18 13 39
Female 10 4 12 26
Total 18 22 25 65

 

  1. The table below shows the number of credit cards owned by a group of individuals. If one person was chosen at random, find the probability that the person had no credit cards.
Zero One Two or more Total
Male 9 5 19 33
Female 18 10 20 48
Total 27 15 39 81
  1. Compute the probability of tossing a six-sided die and getting an even number.
  2. Compute the probability of tossing a six-sided die and getting a number less than 3.
  3. If you pick one card at random from a standard deck of cards, what is the probability it will be a King?
  4. If you pick one card at random from a standard deck of cards, what is the probability it will be a Diamond?
  5. Compute the probability of rolling a 12-sided die and getting a number other than 8.
  6. If you pick one card at random from a standard deck of cards, what is the probability it is not the Ace of Spades?
  7. Referring to the grade table from question #7, what is the probability that a student chosen at random did NOT earn a C?
  8. Referring to the credit card table from question #8, what is the probability that a person chosen at random has at least one credit card?
  9. A six-sided die is rolled twice. What is the probability of showing a 6 on both rolls?
  10. A fair coin is flipped twice. What is the probability of showing heads on both flips?
  11. A die is rolled twice. What is the probability of showing a 5 on the first roll and an even number on the second roll?
  12. Suppose a jar contains 17 red marbles and 32 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.
  13. Suppose you write each letter of the alphabet on a different slip of paper and put the slips into a hat. If you pull out two slips at random, find the probability that both are vowels.
  14. Bert and Ernie each have a well-shuffled standard deck of 52 cards. They each draw one card from their own deck. Compute the probability that:
    1. Bert and Ernie both draw an Ace.
    2. Bert draws an Ace but Ernie does not.
    3. neither Bert nor Ernie draws an Ace.
    4. Bert and Ernie both draw a heart.
    5. Bert gets a card that is not a Jack and Ernie draws a card that is not a heart.
  15. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
    1. Bert gets a Jack and Ernie rolls a five.
    2. Bert gets a heart and Ernie rolls a number less than six.
    3. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
    4. Bert gets a red card and Ernie rolls a fifteen.
    5. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
  16. Compute the probability of drawing a King from a deck of cards and then drawing a Queen.
  17. Compute the probability of drawing two spades from a deck of cards.
  18. A math class consists of 25 students, 14 female and 11 male.  Two students are selected at random to participate in a probability experiment.  Compute the probability that
    1. a male is selected, then a female.
    2. a female is selected, then a male.
    3. two males are selected.
    4. two females are selected.
    5. no males are selected.
  19. A math class consists of 25 students, 14 female and 11 male.  Three students are selected at random to participate in a probability experiment.  Compute the probability that
    1. a male is selected, then two females.
    2. a female is selected, then two males.
    3. two females are selected, then one male.
    4. three males are selected.
    5. three females are selected.
  20. Giving a test to a group of students, the grades and gender are summarized below. If one student was chosen at random, find the probability that the student was female and earned an A.
A B C Total
Male 8 18 13 39
Female 10 4 12 26
Total 18 22 25 65
  1. The table below shows the number of credit cards owned by a group of individuals. If one person was chosen at random, find the probability that the person was male and had two or more credit cards.
Zero One Two or more Total
Male 9 5 19 33
Female 18 10 20 48
Total 27 15 39 81
  1. A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is red or odd-numbered.
  2. A jar contains 4 red marbles numbered 1 to 4 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability the marble is blue or even-numbered.
  3. Referring to the table from #29, find the probability that a student chosen at random is female or earned a B.
  4. Referring to the table from #30, find the probability that a person chosen at random is male or has no credit cards.
  5. Compute the probability of drawing the King of hearts or a Queen from a deck of cards.
  6. Compute the probability of drawing a King or a heart from a deck of cards.
  7. A jar contains 5 red marbles numbered 1 to 5 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is
    1. Even-numbered given that the marble is red.
    2. Red given that the marble is even-numbered.
  8. A jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is
    1. Odd-numbered given that the marble is blue.
    2. Blue given that the marble is odd-numbered.
  9. Compute the probability of flipping a coin and getting heads, given that the previous flip was tails.
  10. Find the probability of rolling a “1” on a fair die, given that the last 3 rolls were all ones.
  11. Suppose a math class contains 25 students, 14 females (three of whom speak French) and 11 males (two of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is female.
  12. Suppose a math class contains 25 students, 14 females (three of whom speak French) and 11 males (two of whom speak French). Compute the probability that a randomly selected student is male, given that the student speaks French.
  13. A jury pool consists of 27 people, 14 men and 13 women. Compute the probability that a randomly selected jury of 12 people is all male.
  14. In a lottery game, a player picks six numbers from 1 to 48. If 5 of the 6 numbers match those drawn, they player wins second prize. What is the probability of winning this prize?
  15. In a lottery game, a player picks six numbers from 1 to 48. If 4 of the 6 numbers match those drawn, they player wins third prize. What is the probability of winning this prize?
  16. Compute the probability that a 5-card poker hand is dealt to you that contains all hearts.
  17. Compute the probability that a 5-card poker hand is dealt to you that contains four Aces.
  18. For the questions below, consider a regular six-sided die.
    1. For rolling a number cube, what are the odds in favor of rolling a number greater than 3?
    2. For rolling a number cube, what are the odds in favor rolling a number less than 5?
    3. For rolling a number cube, what are the odds against rolling a number less than 5?
    4. For rolling a number cube, what are the odds in favor of rolling an even number?
    5. For rolling a number cube, what are the odds against rolling an even number?

    For a spinner numbered 1 –10, answer the following questions.

    1. For spinning the spinner, what are the odds in favor of the arrow landing on 10?
    2. For spinning the spinner, what are the odds in favor of the arrow landing on a 2 or 3?
    3. For spinning the spinner, what are the odds in favor of the arrow landing on 7, 8 or 9?
    4. For spinning the spinner, what are the odds in favor of NOT landing on an even number?
    5. For spinning the spinner, what are the odds of the arrow NOT landing on 10?
    6. For spinning the spinner, what are the odds in favor of the arrow landing on a number greater than 2?
    7. For spinning the spinner, what are the odds in favor of the arrow NOT landing on a number greater than 2?
    8. For spinning the spinner, what are the odds of the arrow not landing on a number greater than 3?