CHECK THE BASICS

For Exercise 19.1, see page 450; for Exercise 19.2, see page 455.

Question 19.3

19.3 Simulations. To simulate random outcomes, we need to know

  1. (a) the probabilities of the outcomes.

  2. (b) whether the probabilities are personal probabilities.

  3. (c) both the mean and standard deviation so we can use the appropriate Normal curve.

  4. (d) that the random outcome has a probability of 0.1 so we can use a table of random digits.

Question 19.4

19.4 A simulation. To simulate the toss of a fair coin (the probability of heads and tails are both 0.5) using a table of random digits,

  1. (a) assign the digits 0, 1, 2, 3, and 4 to represent heads and the digits 5, 6, 7, 8, 9 to represent tails.

  2. (b) assign the digits 0, 2, 4, 6, and 8 to represent heads and the digits 1, 3, 5, 7, and 9 to represent tails.

  3. (c) assign the digits 0, 1, 5, 8, and 9 to represent heads and the digits 2, 3, 4, 6, and 7 to represent tails.

  4. (d) use any of the above. All are correct.

457

Question 19.5

19.5 Independence. Two random phenomena are independent if

  1. (a) knowing that one of the outcomes has occurred means the other cannot occur.

  2. (b) knowing the outcomes of one does not change the probabilities for outcomes of the other.

  3. (c) both have the same probability of occurring.

  4. (d) both have different and unrelated probabilities of occurring.

Question 19.6

19.6 Elaborate simulations. A tree diagram

  1. (a) was originally used by biologists for simulations involving trees.

  2. (b) is used to determine if two random phenomena are independent.

  3. (c) is used when two random phenomena are independent.

  4. (d) specifies a probability model in graphical form.

Question 19.7

19.7 Elaborate simulations. The key to successful simulation is

  1. (a) keeping the tree diagram as simple as possible.

  2. (b) thinking carefully about the probability model for the simulation.

  3. (c) using as few trials as possible so that the chance of an incorrect trial is kept small.

  4. (d) using all the digits in a random digits table.