`01:00`

STAT 20: Introduction to Probability and Statistics

- Concept Questions
- Break
- Handout: PS 3.3a (computing probabilities)
- Break
- Two useful R functions
- Digital worksheet: PS 3.3b (simulating probabilities)

`01:00`

I have a box with 12 cards in it. Four of the cards are red, four are blue, and four are green. I shuffle the cards in the box, and draw one out at random. The outcome of the card being green and the outcome of the card being red are _____.

`02:00`

The Houston Astros beat the Philadelphia Phillies in the 2022 World Series. The winners in the World Series have to win a majority of 7 games, so the first team to win 4 games wins the series (best of 7). The Astros were heavily favored to win, so the outcome wasn’t really a suprise. Suppose we assumed that the probability that the Astros would have beaten the Phillies in any single game was estimated at 60%, independently of all the other games, what was the probability that the Astros would have won in a clean sweep?

(Clean sweep means that they won in the first 4 games - which didn’t happen, they won in 6 games.)

`01:00`

Suppose we assume, instead, that the probability that the Astros would have beaten the Phillies in any single game was 50%, independently of all the other games. In this case, was the probability that the series would have gone to 6 games higher than the probability that the series would have gone to 7 games, **given** that 5 games were played?

`03:00`

On each turn of a game, I toss a coin as many times as the number of spots I get when I roll a die. On a turn what is the probability that all my tosses land heads? Is it true that it is \(\left(\frac{1}{2}\right)^k\), where \(k\) is the number of spots from the die I just rolled? (Be careful! are you being asked for a conditional probability?)

`03:00`

A rare condition affects **0.2%** of the population. A test for this condition is 99% accurate: this means that the probability that a person *with* the condition tests positive is 99% and the probability that a person *without* the condition tests negative is 99%. What is the probability that a person who tests positive has the condition?

`05:00`

`25:00`

`seq()`

Creates a sequence of numbers that can be defined by their first and last number and the space between each number (or the total numbers in the sequence): `seq(from, to, by)`

**Code Along**

How can you use `seq()`

to generate the following sequence: 1, 1.25, 1.5, 1.75, 2 and call it `a`

?

`01:00`

`sample()`

Used to take a random sample of a vector with or without replacement: `sample(x, size, replace = FALSE)`

**Code Along**

How can you use `sample()`

to create the following vector from `a`

: 1.25, 1.25, 1.50.

When we want a specific sample, or want the same sample every time we run our code, we use the function `set.seed()`

. This initializes R’s pseudorandom number generator, so that when you are running simulations or code that requires random sampling, you can reproduce your results.

`05:00`

`30:00`