example 1

• Of six envelopes, three each hold $1, two each hold $1000, and one holds $100 000. You choose one of the envelopes at random and get to keep the contents. Calculate the expected value of the contents interpret its meaning. What is the expected value if you add $10 000 to each envelope? If you multiply the amount in each envelope by 10?

example2

• Two blocks are drawn randomly from a bag containing 12 blue blocks and 19 red blocks. What is the probability that the two blocks are both blue if the ?rst block is replaced before the second block is drawn? If the ?rst block is not replaced before the second is drawn?

example3

• Simulate flipping a fair coin and biased coin 100 times. What does fair and biased mean in the context of flipping? Graph and compare results.

example4

• Compare the probability distributions associated with drawing 0, 1, 2, or 3 diamonds when a card is drawn 4 times from a standard deck (i) when the card is replaced after each draw and (ii) when the card is not replaced after each draw.

example5

• Two dice are rolled and the sum is determined. Define a discrete random variable representing the sum and generate the related probability histogram. What is the total area of the bars in the histogram?

example6

• Two dice are rolled and the sum is determined. Simulate the experiment 1000 times and calculate the experimental probability of each outcome. Compare with the theoretical probabilities.

example7

• Calculate the theoretical probability of rolling a 4 on a single roll of a die. Simulate rolling a die, and use the results to calculate the experimental probabilities of rolling a 4 over 10, 20,… ,200 trials. Graph the experimental probabilities versus the number of trials.