Probability

Principle of Inclusion and Exclusion

Principle of Inclusion and Exclusion - Two Sets

         

Two standard six-sided dice, one red and one blue, are rolled. How many different rolls are there in which at least one dice shows a 55?

If AA and BB are two sets such that AB=45,AB=21 and AB=11,\lvert{A \cup B}\rvert=45, \lvert{A \cap B}\rvert=21 \text{ and } \lvert{A \setminus B}\rvert=11, then what is the value of B?\lvert{B}\rvert?

Details and assumptions

You may choose to read the summary page Set Notation.

Calvin has 23 books on his shelf, all of which are either Mathematics books or hardcover books. If 18 of the 23 are hardcover books, and 12 of the 23 are Mathematics books, how many hardcover Mathematics books does Calvin have on his shelf?

Details and assumptions

You may choose to read Principle of Inclusion and Exclusion.

If set AA contains 5757 elements, set BB contains 316316 elements and ABA \cap B contains 1515 elements, how many elements are contained in AB?A \cup B?

Details and assumptions

You may choose to read the summary page Set Notation.

In a group of 5252 students, 3838 are taking physics and 4747 are taking chemistry. If xx is the number of students taking both physics and chemistry, then the possible range of xx is axb.a \leq x \leq b. What is ba?b-a?

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