2.1.3.2.2 - Intersections

Intersection

The overlap of two or more events is symbolized by the character \(\cap\). 

\(P(A \cap B)\) is read as "the probability of A and B."

Intersection of A and B

Example: Red King Section

What is the probability of randomly selecting a card from a standard 52-card deck that is a red card and a king?

There are 2 kings that are red cards: the king of hearts and the king of diamonds.

\(P(red \cap king)=\dfrac{2}{52}=.0385\)

Example: Female Undergraduate Students Section

The two-way table below displays the World Campus enrollment from Fall 2015 in terms of level (undergraduate and graduate) and biological sex. What proportion of World Campus students were female and undergraduate students?

  Female Male Total
Undergraduate 3814 3428 7242
Graduate 2213 2787 5000
Total 6027 6215 12242

There are 3814 students who are females and undergraduates out of a total of 12242 students.

\(P(F \cap U)=\dfrac{3814}{12242}=0.312\)