PROBABILITY

# Conditional probability

Given two events, A and B, the **conditional probability of B given A** is:

Example: this table shows the distribution of percentages of the Spanish people’s blood group. Calculate the probability of having B group and the same probability if you know that the RhD is +.

If we work out:

Two events are

**independent**if:otherwise, they are **dependent**.

Then, if A and B are independent events:

Example 1: If we flip two coins, the events:

A = {H- 1

^{st}throw} B = {T- 2^{nd}throw} are independent becauseExample 2: We extract two cards (without replacement) out of a Spanish pack of 40 cards. Let the events:

A = {gold- 1st extraction} B = {cup- 2nd extraction}

Are they independent?

They are dependent events

Example 3: In a city, 40% of the people usually watch TV, 10% usually read a book and 1% do both things regularly.

a) If we choose a person randomly, what is the probability that he or she watches TV or reads a book regularly?

b) If we choose a person at random and he or she usually watches TV, what is the probability that he or she usually reads a book?

**Exercise**: In a school, 30% of the students play basketball, 40% play football and 50% play one of them or both.

a) If we choose a student randomly, what is the probability that he or she plays football and basketball?

b) If we choose a student randomly and he or she plays basketball, what is the probability that he or she plays football as well?

Solutions: a) 0.2; b) 0.67

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