# Question: Using the Simulating the Probability of a Head With a

Using the Simulating the Probability of a Head With a Fair Coin applet on the text CD or other software, simulate the flipping of a balanced coin.

a. Report the cumulative proportion of heads after (i) 10 flips, (ii) 100 flips, (iii) 1000 flips, and (iv) 10,000 flips. Explain how the results illustrate the law of large numbers and the long-run relative frequency definition of probability.

b. Using the Simulating the Probability of Rolling a 3 or 4 applet or other software, simulate the roll of a die with a success defined as rolling a 3 or 4, using (i) 10 rolls, (ii) 100 rolls, (iii) 1000 rolls, and (iv) 10,000 rolls. Summarize results.

a. Report the cumulative proportion of heads after (i) 10 flips, (ii) 100 flips, (iii) 1000 flips, and (iv) 10,000 flips. Explain how the results illustrate the law of large numbers and the long-run relative frequency definition of probability.

b. Using the Simulating the Probability of Rolling a 3 or 4 applet or other software, simulate the roll of a die with a success defined as rolling a 3 or 4, using (i) 10 rolls, (ii) 100 rolls, (iii) 1000 rolls, and (iv) 10,000 rolls. Summarize results.

## Relevant Questions

a. What is a sample space? Give an example of a sample space for a scenario involving (i) a designed experiment and (ii) an observational study. b. What are disjoint events? Give an example of two events that are ...From past experience, a wheat farmer living in Manitoba, Canada finds that his annual profit (in Canadian dollars) is $80,000 if the summer weather is typical, $50,000 if the weather is unusually dry, and $20,000 if there is ...For a normal distribution, use Table A to verify that the probability (rounded to two decimal places) within a. 1.64 standard deviations of the mean equals 0.90. b. 2.58 standard deviations of the mean equal 0.99. c. Find ...According to Current Population Reports, self-employed individuals in the United States work an average of 44.6 hours per week, with a standard deviation of 14.5. If this variable is approximately normally distributed, find ...Refer to the normal distributions for women’s height (μ = 65, σ = 3.5) and men’s height (μ = 70, σ = 4.0). A man’s height of 75 inches and a woman’s height of 70 inches are both 5 inches above their means. Which ...Post your question