Probability & Statistics for Machine Learning & Data Science (2)

Introduction to Probability and Probability Distributions

Introduction to Probability

A sum of Probabilities (Disjoint Events)

We can add the probabilities for disjoint events to obtain the result (a probability of a union).

Disjoint means they cannot occur simultaneously (no overlapping).

What is the probability that a kid plays soccer or basketball?

0.7

01

When throwing a 6-sided dice, what is the probability of obtaining an even number or a 5?

2/3

If you roll two fair dice, what is the probability of obtaining a sum of 7 or 10?

9/36

If you roll two fair dice, what is the probability of obtaining a difference of 2 or a difference of 1?

18/36

A sum of Probabilities (Joint Events)

For joint events, we subtract the intersection from the union of events.

Joint means events can overlap.

What is the probability that a kid plays soccer or basketball?

We cannot tell with the information given.

Correct. Since we do not know how many play soccer and basketball, we cannot infer the desired probability.

01

How many kids play soccer or basketball?

8

Correct! We know This is because 5 + 6 - 3 = 8!

01

In a school, we know that the probability that a kid plays soccer is 0.6, the probability that a kid plays basketball is 0.5 and the probability that a kid plays both soccer and basketball is 0.3. What is the probability that a child plays soccer or basketball?

0.8

01

If you rolled two fair die, what is the probability of obtaining a sum of 7 or a difference of 1?

14/36

Independence

Independence happens when the occurrence of one event does not affect the probability of the occurrence of another event.

Assuming that things are independent helps us simplify calculations and make predictions.

In a school with 100 kids, where 50 like soccer and 50 don't, if we randomly split the kids in two rooms with 50 kids each, what is your best estimate on the number of kids in room 1 that like soccer?

25

In a school with 100 kids, where 40 like soccer and 60 don't, if we randomly split the kids in two rooms with 30 kids in one room and 70 in the other, what is your best estimate on the number of kids in room 1 that like soccer?

12

We multiply probabilities if the events are independent.

If you toss a fair coin 5 times, what is the probability of landing heads 5 times?

1/32

If you roll a fair die 10 times, what is the probability of getting 10 sixes?

$({1\over6})^{10}$

Birthday problem

You have 30 friends in a party. What do you think is more likely?

There exist at least two people with the same birthday.

01

As we multiply the probability of having different birthdays, the probability of not having two people with the same birthday gets lower and eventually gets close to 0.

 

All the information provided is based on the Probability & Statistics for Machine Learning & Data Science | Coursera from DeepLearning.AI