STAT 20: Introduction to Probability and Statistics

- Concept Questions
- Activity: coin tosses
- Handout

`01:00`

Suppose Ali and Bettina are playing a game, in which Ali tosses a fair coin \(n\) times, and Bettina wins one dollar from Ali if the proportion of heads is less than 0.4. Ali lets Bettina decide if \(n\) is 10 or 100.

Which \(n\) should Bettina choose?

`02:00`

Consider the box of tickets shown below.

The plots below show:

- The probability histogram for the value of a ticket drawn at random from the box
- An empirical histogram for which the data were generated by drawing
**10**tickets from the box with replacement - An empirical histogram for which the data were generated by drawing
**100**tickets from the box with replacement - An empirical histogram generated by
**20**draws from a different box.

Identify which is which by matching the letters to the numbers.

Part 1: Suppose we roll a die 4 times. The chance that we see six (the face with six spots) at least once is given by \(\displaystyle \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3}\)

True or false?

Part 2: Suppose we roll a pair of dice 24 times. The chance that we see a pair of sixes at least once is given by \(\displaystyle 24 \times \frac{1}{36} = \frac{24}{36} = \frac{2}{3}\)

True or false?

`02:00`

`01:00`

Consider the Venn diagram below, which has 20 possible outcomes in \(\Omega\), depicted by the purple dots. Suppose the dots represent equally likely outcomes. What is the probability of \(A\) or \(B\) or \(C\)? That is, what is \(P(A \cup B \cup C)\)?

`25:00`