Thank you everyone for participating in our rationality poll! We received over 500 responses. Here are the poll results and answers to our previous article on rationality.

#### Question 1

Consider a coin toss with an equal probability of landing either heads (“H”) or tails (“T”) up, which event is more likely to happen?

(Both events are the same number of tosses)

Event 1: HHHHHTTTTT

Event 2: HTHTHTHTHT

Correct Answer: Equally likely. Event 2 seems more random and hence more probable. However, remember that the coin tosses are independent events. The chance of getting tails is always the same, even after tossing consecutive heads. Do not confuse the likelihood of Event 1 with mean reversion; mean reversion applies to non-independent events.

#### Question 2

Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Which of the following is more probable?

Option 1: Linda is a bank teller

Option 2: Linda is a bank teller and is active in the feminist movement.

Correct Answer: Linda is a bank teller. The description suggests that Linda has the inclination towards feminist movement. Unfortunately, it is an axiom of probability that an event with more conditions (‘active in the feminist movement’) cannot be more probable than the base event itself (‘bank teller’).

#### Question 3

Rate your athletic ability in relation to the average person

Seems like our readers are rational, kudos! This question was intended to demonstrate overconfidence bias. Previous studies have shown that majority of respondents indicate that they have ‘Above average’ athletic ability. This portends overconfidence, as by definition, the majority should be the average.

#### Question 4

2 hospitals, one in big town and one in small town, track the proportion of male and females babies born. Which has higher likelihood of having skewed proportions?

Correct Answer: Small town. The law of small numbers is at play here. A smaller sample size has a higher probability of having skewed or data points that are unrepresentative of the larger population. Imagine a series of 3 coin tosses; it would be impossible to get a 50-50 split between heads and tails. The probability of heads or tails, as demonstrated by the 3 coin tosses, would be about 67% instead.