Probability problems

  1. A card is to be dealt from a shuffled deck. What is the probability that it will be the Ace of Clubs?
    1. What is the probability that it will be a Club?
    2. What is the probability that it will be a face card?
    3. What is the probability that it will be a face card and a club?
    4. What is the probability that it will be a face card or a club?
    5. What is the probability of dealing some card?
    6. What is the probability of dealing a hockey card?
  2. A coin is tossed 7 times, what is the probability of getting 4 heads and 3 tails? What is the probability of getting 4 or more heads?
  3. An urn contains 40 balls some red and the others white. The probability of drawing a red ball is 0.45. How many red balls are in the urn?
  4. Another urn contains 5 red and 4 white balls. Two balls are drawn from it. What is the probability that at least one of them is red?
  5. A factory produces fuses, which are packaged 10 to a box. The quality control system is to select three fuses from each box to test, and to reject the box if any of the three are defective. What is the probability that a box with 5 bad fuses will be detected and rejected?
  6. In poker the probabilities of being dealt a flush, a straight, and a straight flush are 0.0019654, 0.0039246 and 0.0000154 respectively. What is the probability of being dealt a straight or a flush?
  7. What is the probability that a random arrangement of the letters in the word GEESE has all the E’s adjacent to one another?
  8. Suppose a certain math class has 26 students (15 first year, 14 business and 7 neither), and that one of them is selected at random.
    1. What is the probability that the student selected is a first year business student?
    2. Suppose we are given the additional information that the person selected is a first-year student, what is the probability that she is also a business student?
  9. A school contains an equal number of male and female students. 5% of the male students are colour-blind. What is the probability that a randomly selected student will be a colour-blind male?
  10. A factory has two machines that produce bolts. Machine I produces 60% of the bolts, 97% of which are good. Machine II produces 40 % of the bolts, 98% of which are good.
    1. What is the probability that a bolt selected at random will be defective?
    2. If a bolt is selected at random and found to be defective, what is the probability that it came from machine I?