Introduction to Probability and Probability Distributions
Introduction to Probability
Conditional Probability - Part 1
Conditional probability is all about calculating the probability of an event happening given that another event has already happened.
What is the probability of landing heads twice if the first coin flip is heads?
1/4
Correct! Given the first coin is head, to get two heads you need one more, which has a probability of 1/2 of happening!
Conditional probability is denoted with a vertical bar “|”
When flipping a coin twice, what is the probability of getting two heads if the first coin lands in tails?
0
Correct! If the first coin lands in tails, it is impossible to get two heads.
The product rule changes slightly when it comes to calculating the conditional probability.
Instead of multiplying two probabilities, we update the second probability to a conditional probability and multiply the two.
Conditional Probability - Part 2
In a school, there are 100 kids, where 50 like football and 50 don't. There are two rooms where in room 1 there is a TV playing a soccer match and in room 2 there is a TV playing a movie unrelated to soccer. Each room fits exactly 50 kids. How many kids that like soccer do you expect to be in room 1?
50
In a school, there are 100 kids. 40 play soccer and 60 don't. Among the 40 that play soccer, 80% of them wear running shoes. How many kids play soccer and wear running shoes?
32
Correct! 80% of 40 is 32.
Random: Independent
Not random: Dependent
If the events are related, then the events are dependent
Bayes’ Theorem - Intuition
Do you think it is more likely for you to be sick or not?
Not sick
Bayes’ Theorem - Mathematical Formula
All the information provided is based on the Probability & Statistics for Machine Learning & Data Science | Coursera from DeepLearning.AI
