Level 6: Conditional probability

Probability · level 6 of 8 · rough age 13-14 (a guide for parents; anyone can start anywhere)

New information changes chances. If you know the card is red, the chance it is a heart jumps from a quarter to a half. This level makes that idea exact with conditional probability, uses it to say precisely what "independent" means, and then puts all the rules to work on some of the most famous puzzles in mathematics: the lottery, the birthday problem and the Monty Hall game show. It ends with chances that are measured by length and area instead of by counting.

Lesson	You will be able to
"Given": conditional probability	Find P(A given B) from a two-way table or a list by shrinking the sample space, and use the formula
Independence, properly	Test whether two events are independent with numbers, and tell independent from mutually exclusive
Probability with combinations	Use combinations to find the chance of a poker hand, a lottery win or a committee chosen by lot
The birthday problem	Show why 23 people are enough for a better than even chance of a shared birthday
The Monty Hall problem	Explain three ways why switching doors wins 2 times out of 3
Geometric probability	Find chances as lengths and areas: darts on a board, waiting for a bus, meeting a friend

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