The following questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including:

• One equal sign per line
• Equal signs in each question lined up vertically with each other

• No self-developed short form notation
• One step or idea per line(do not do steps in your head that are not written down; each line must represent a step-by-step progression from question to answer)

Please include neat, complete solutions showing all the steps you used to get your final answer. Be sure your graphs are well labeled, and your curves each easily distinguished with colour coding if you have more than one curve on a grid.

1. During a recent survey of ethnic backgrounds of 1000 people in a large city, 513 were Canadian, 148 were French, 72 were African and 56 were Asian and the remainder were from other groups.ESRC.AC.UKCalculate the probability that a person, selected at random from the population has:
   1. a Canadian background?
   2. an African background?
   3. an other background?
   6 marks
2. A SpinnerA spinner is divided into three equally sized regions as shown. The spinner is spun twice. For each probability you determine, express your answer as a fraction, decimal and percent.
   1. What is the probability of spinning A on the first spin?
   2. Draw a tree diagram to represent the sample space for both spins.
   3. What is the probability of spinning A followed by B?
   4. What is the probability of getting the same letter on both spins?
   6 marks
3. We have looked in detail at three probability distributions;
   • binomial
   • geometric
   • hypergeometric
   For each one,
   1. Explain the conditions in which we would use it.
   2. Justify the formula used.
   3. Give an example of a situation in which it could be used.
   8 marks
4. Two standard six-sided dice are rolled. One die is blue and the other is red.NCETM.ORG:
   1. Create a table to represent the sample space
   2. For each probability below, express the answer as a fraction, as a decimal, and as a percentage.
      1. What is the probability of rolling a sum greater than ten?
      2. What is the probability that the number on the red die is one larger than the number on the blue die?
      3. What is the probability that the sum of the two numbers is less then 11?
   8 marks
5. Use a tree diagram to explain why the probability that a family with four children all have the same gender is. Assume that the probability of having a girl is equal to the probability of having a boy.3 marks
6. In a library box, there are 8 novels, 8 biographies and 8 war history books. If Jack selects two books at random, what is the probability that the two books are of different types? 3 marks
7. The probability that Prasha will score above a 90 on a mathematics test is. What is the probability that she will score above a 90 on exactly 3 of the 4 tests this quarter? 4 marks
8. A company manufacturing laptops believes that 5% of their computers are faulty. They take a sample of 30 computers. Showing your calculations, find the probability that;
   1. Two of the laptops are faulty.
   2. More than two of the laptops are faulty.
   4 marks
9. There are six cats and seven dogs in the local animal shelter. Four animals are chosen at random to visit a local school to educate the children on the great need for homes for these animals. FUNXITE.COMA friendly dog and cat
   1. What is the probability that exactly two of the animals are cats?
   2. What is the probability that at least one cat is chosen?
   6 marks
10. TEENRANCH.COMA certain hockey player scores on 18% of his shots.
    1. What is the probability he will score for the first time on his fifth shot?
    2. What is the probability that it will take him fewer than 3 shots to score?
    3. How many shots should he expect to take before scoring?
    6 marks
11. In a multiple choice quiz, there are 6 questions. Each question has 5 possible answers. A student guesses at each question.
    1. Find the probability that the student gets 4 answers correct.
    2. Find the probability that the student passes(i.e. gets at least 50%)
    3. What is the student's expected number of correct answers?
    6 marks