Discrete Probability and Independence Questions

Saturday, 11 December 2021 / Published in Uncategorized

Discrete Probability and Independence Questions

Try the following questions on discrete probability and independence. The correct anwers are revealed when you submit your answers.

1. Suppose you toss a coin twice in a row showing either heads (\( H \)) or tails (\( T \)) on each toss, for example the outcome could be a tail followed by a head \( (T,H) \). What is the sample space?

\( \Omega = \{(H,T), (H,H), (T,H), (T,T)\} \)

\( \Omega= \{ (H,H), (T,H), (T,T)\} \)

\( \Omega= \{ (H,T,H) \} \)

\( \Omega= \{ H,T \} \)

2. On a roll of a die what is the probability of getting less than \( 4 \)?

\( \frac{1}{6} \)

\( \frac{1}{2} \)

\( \frac{5}{6} \)

\( 1 \)

3. The probability it rains on Sunday given that it rained on Saturday is \( \frac{2}{3} \).
The probability it rains on Saturday is \( \frac{1}{3} \). What is the probability it rains on Saturday and doesn't rain on Sunday?

\( \frac{1}{2} \)

\( \frac{2}{3} \)

\( \frac{1}{3} \)

\( \frac{1}{9} \)

Probability Table Of Contents

Part 0: Preliminaries

0.1 Set Notation
0.2 Permutations and Combinations
Questions

Part 1: Probability

1.1 Discrete Probability
1.2 Independence and Conditional Probabilities
Questions
1.3 Bayes Theorem
1.4 Inclusion Exclusion Principle
1.5 Discrete Random Variables
- 1.51 Indicator Functions
1.6 Bernoulli Trials and the Binomial Distribution
1.7 Poisson Distribution
1.8 Poisson Process
1.9 Joint Probability Distribution
2.0 Continuous Random Variables

2.01 Joint Density Function
2.02 The Normal Distribution
2.03 The Log-Normal Distribution

2.1 Generating Functions

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