Checkbox

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 is more probable?

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

Submit Show Hint Show Answer Clear Think about the probabilities of each event, and that of both of them together.

If you chose (2), stop back and think. Suppose we denote the event of Linda being a teller by A and the event she is active in the feminist movement by B, then probabilities in question can be written as.

P(A)\(P(A \cap B)\)

This is called the conjugacy fallacy that occurs when it is assumed that specific conditions are more probable than a single general one.

--- &checkbox

## Checkbox

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 is more probable?

1. _Linda is a bank teller._2. Linda is a bank teller and is active in the feminist movement.

*** .hint

Think about the probabilities of each event, and that of both of them together.

*** .explanation

If you chose (2), stop back and think. Suppose we denote the event of Linda being a teller by A and the event she is active in the feminist movement by B, then probabilities in question can be written as.

- P(A)- $P(A \cap B)$

This is called the [conjugacy fallacy](http://en.wikipedia.org/wiki/Conjunction_fallacy) that occurs when it is assumed that specific conditions are more probable than a single general one.

Multi Text

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.

What percent of pregnancies last fewer than 240 days?What percent of pregnancies last between 240 and 270 days?How long do the longest 25% pregnancies last?

Submit Show Hint Show Answer Clear 5.208154.6625276.7918

This is a hint

--- &multitext

## Multi Text

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days.

1. What percent of pregnancies last fewer than 240 days?2. What percent of pregnancies last between 240 and 270 days?3. How long do the longest 25% pregnancies last?

*** .explanation

1. `r pnorm(240, 266, 16)*100`2. `r (pnorm(270, 266, 16) - pnorm(240, 266, 16))*100`3. `r qnorm(0.25, 266, 16, lower.tail = F)`>

*** .hint

This is a hint

Submit and Compare What is the sample space for this experiment?

Submit and Compare

Clear

The sample space for this experiment is

{HH, HT, TH, HH}

--- &submitcompare1

## Submit and Compare

What is the sample space for this experiment?

*** .explanation

The sample space for this experiment is

{HH, HT, TH, HH}

Submit and Compare (2 Column)

The solid curve represents the distribution of heights of all males in the US. The dotted curve represents the distribution of heights reported by males on OkCupid, an online dating website.

What is happening here?

Submit and Compare Clear It is easier to interpret things if we overlay a fitted normal distribution for the heights reported by males on OkCupid. Looking at the graph carefully, we can observe two things.

Males on OkCupid probably tend to inflate their heights!You can also see a more subtle vanity at work: starting at roughly 5' 8", the top of the dotted curve tilts even further rightward. This means that guys as they get closer to six feet round up a bit more than usual, stretching for that coveted psychological benchmark.

--- &submitcompare2 rows:5

## Submit and Compare (2 Column)

The solid curve represents the distribution of heights of all males in the US. The dotted curve represents the distribution of heights reported by males on OkCupid, an online dating website.

*** =question

What is happening here?

*** .explanation

It is easier to interpret things if we overlay a fitted normal distribution for the heights reported by males on OkCupid. Looking at the graph carefully, we can observe two things.

1. Males on OkCupid probably tend to inflate their heights!2. You can also see a more subtle vanity at work: starting at roughly 5' 8", the top of the dotted curve tilts even further rightward. This means that guys as they get closer to six feet round up a bit more than usual, stretching for that coveted psychological benchmark.

-->