The phrase “coin toss” is a classic synonym for randomness. But since at least the 18th century, mathematicians have suspected that even fair coins tend to land on one side slightly more often than the other. Proving this tiny bias, however, would require hundreds of thousands of precisely recorded coin flips, making laboratory tests a logistical nightmare.

František Bartoš, currently a Ph.D. candidate studying the research methods of psychology at the University of Amsterdam, became intrigued by this challenge four years ago. He couldn’t round up enough volunteers to investigate it at first. But after he began his Ph.D. studies, he tried again, recruiting 47 volunteers (many of them friends and fellow students) from six countries. Multiple weekends of coin flipping later, including one 12-hour marathon session, the team had performed 350,757 tosses, shattering the previous record of 40,000. The flipped coins landed with the same side facing upward as before the toss 50.8 percent of the time. The large number of throws allows statisticians to conclude that the nearly 1 percent bias isn’t a fluke. “We can be quite sure there is a bias in coin flips after this data set,” Bartoš says.

The leading theory explaining the subtle advantage comes from a 2007 physics study by Stanford University statistician Persi Diaconis and his colleagues, whose calculations predicted a same-side bias of 51 percent. From the moment a coin is launched into the air, its entire path — including whether it lands on heads or tails — can be calculated by the laws of mechanics. The researchers determined that coins in the air don’t turn around their center line; instead they tend to shake off-center, which causes them to spend a little more time aloft with their initial “up” side on top.

1.1. Why was it hard to prove the coin flip bias initially?

A The bias was surprisingly large.

B The theory lacked clarity.

C Enough data was difficult to get.

D The experiment was expensive.

解析：选C。1.C细节理解题。第一段明确指出“Proving this tiny bias, however, would require hundreds of thousands of precisely recorded coin flips, making laboratory tests a logistical nightmare.”（“证明这种微小偏差需要数十万次精确记录的抛掷，这使得实验室测试成为后勤上的难题”），说明最初的困难在于难以获取足够数据。故选C。

2.2. What did Bartoš’s experiment with over 350,000 flips prove?

A There is strength in numbers.

B Flipping techniques vary widely.

C More throws reduce the bias.

D Coin flips show a small but real bias.

解析：选D。2.D细节理解题。第二段给出实验结果：350,757次抛掷中“landed with the same side facing upward as before the toss 50.8 percent of the time”（同一面朝上的概率为 50.8%），并指出“the nearly 1 percent bias isn’t a fluke”（这近1%的偏差并非偶然），“We can be quite sure there is a bias in coin flips after this data set”（基于这组数据，我们可以非常确定抛硬币存在偏差），因此D项“抛硬币存在虽小却真实的偏差”正确。故选D。

3.3. What is Paragraph 3 mainly about?

A The math model behind the experiment.

B Diaconis’s theory has been widely accepted.

C The physical cause of the coin bias.

D More flips remove all doubt.

解析：选C。3.C段落大意题。第三段介绍2007年物理学研究，指出“from the moment a coin is launched into the air, its entire path…can be calculated by the laws of mechanics”（“从硬币被抛向空中的那一刻起，其整个运动轨迹……都可以用力学定律计算”），并解释偏差原因：“coins in the air don’t turn around their center line; instead they tend to shake off-center, which causes them to spend a little more time aloft with their initial ‘up’ side on top”（“空中的硬币并不绕其中心轴翻转，而是倾向于偏心晃动，这使得初始朝上的一面在空中停留的时间略长”）。整段围绕硬币偏差的物理成因展开。故选C。

4.4. What is Amelia’s attitude to the new study’s findings?

A Professionally appreciative.

B Cautiously dismissive.

C Totally indifferent.

D Mostly confused.

解析：选A。4.A观点态度题。末段统计学家阿米莉亚·麦克纳马拉虽未参与研究，但评价该研究“should clear away any remaining doubt regarding the coin flip’s slight bias”（“应能消除对抛硬币微小偏差的任何残留疑虑”），并称“This is great evidence based on experiments backing that up”（“这是基于实验支持的极好证据”），表现出从专业角度对研究证据的欣赏与肯定。故选A。