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# 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- 1st throw}   B = {T- 2nd throw} are independent because

Example 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