If a piece of toast falls off your breakfast plate, is it more likely to land with the buttered side down? According to Murphy’s Law (the assumption that if anything can go wrong, it will), the answer is “Yes.” Most scientists would argue that by the law of probability, the toast is equally likely to land butter-side up or butter-side down. Robert Matthews, science correspondent of the Sunday Telegraph, disagrees. He claims that when toast falls off a plate that is being carried at a “typical height,” the toast has just enough time to rotate once (landing butter-side down) before it lands. To test his claim, Mr. Matthews has arranged for 150,000 students in Great Britain to carry out the experiment with tumbling toast.

Question

If a piece of toast falls off your breakfast plate, is it more likely to land with the buttered side down? According to Murphy’s Law (the assumption that if anything can go wrong, it will), the answer is “Yes.” Most scientists would argue that by the law of probability, the toast is equally likely to land butter-side up or butter-side down. Robert Matthews, science correspondent of the Sunday Telegraph, disagrees. He claims that when toast falls off a plate that is being carried at a “typical height,” the toast has just enough time to rotate once (landing butter-side down) before it lands. To test his claim, Mr. Matthews has arranged for 150,000 students in Great Britain to carry out the experiment with tumbling toast.

Assuming scientists are correct, the proportion of times that the toast will land butter-side down is p = 0.5. We can use a coin toss to simulate the experiment. Let heads represent the toast landing butter-side up.

a) Toss a coin 5 times and record the proportion of heads obtained, (number of heads)/5. Explain how your result relates to the tumbling-toast experiment.

b) Repeat this sampling process 5 times. Make a dotplot of the 5 values of . Is the center of your distribution close to 0.5?

Answer 1

We cannot toss the coins for you nor make a plot.

Answer 2

a) To simulate the tumbling-toast experiment, we can use a coin toss. In this case, let's consider heads to represent the toast landing butter-side up.

Toss the coin 5 times, and record the proportion of heads obtained. The proportion is calculated as the number of times the coin landed heads divided by the total number of coin tosses.

For example, if the results of the coin tosses were heads, tails, heads, heads, heads, then the proportion of heads obtained would be 4/5 or 0.8.

This approach relates to the tumbling-toast experiment because the proportion of heads obtained in the coin toss simulation represents the probability of the toast landing butter-side up. In the same way, by calculating the proportion of times the toast lands butter-side up in the tumbling-toast experiment, we can estimate the probability of this happening.

b) Repeat the sampling process of tossing a coin 5 times multiple times, let's say 5 times in this case. Record the proportions obtained from each set of 5 tosses.

For example, after repeating the sampling process 5 times, you may get the following proportions: 0.4, 0.6, 0.8, 0.2, 0.6.

To visualize the distribution of these proportions, create a dot plot. Each dot on the plot represents one set of 5 coin flips, and the position on the vertical axis represents the proportion obtained.

The center of the distribution is represented by the average or mean of the proportions. Calculate the mean of the 5 proportions obtained. If the mean is close to 0.5, it suggests that the distribution is centered around the expected probability of the toast landing butter-side up.

For example, if the mean of the 5 proportions is 0.52, it indicates that the center of the distribution is slightly above 0.5. In this case, the distribution is close to the expected probability of the toast landing butter-side up according to the scientists' argument.