Statistics 5.3 Trees and Counting Principle

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all possible outcomes of an event, helping to organize and count outcomes systematically.

Front

What is the fundamental counting principle?

Back

The fundamental counting principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in m × n ways.

Front

How many outcomes are there if a coin is flipped 3 times?

Back

There are 2^3 = 8 outcomes.

Front

What is the formula for permutations of 'n' items taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

What is the formula for combinations of 'n' items taken 'r' at a time?

Back

The formula is C(n, r) = n! / [r!(n - r)!].

Front

How many different ways can 5 books be arranged on a shelf?

Back

There are 5! = 120 ways to arrange 5 books.

Front

What is the total number of possible license plates with 6 characters (0-9, A-Z)?

Back

There are 36 options (10 digits + 26 letters) for each character, so 36^6 = 2176782336 possible license plates.

Front

If a shirt can be chosen in 3 ways, pants in 2 ways, and shoes in 2 ways, how many outfits can be made?

Back

The total number of outfits is 3 × 2 × 2 = 12.

Front

What is the difference between experimental probability and theoretical probability?

Back

Experimental probability is based on actual experiments or trials, while theoretical probability is based on the expected outcomes in a perfect scenario.

Front

How many ways can a coach arrange a batting order for 10 players?

Back

There are 10! = 3628800 ways to arrange a batting order for 10 players.