Probability and combinations

Front

What is the definition of probability?

Back

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter.

Front

What is a permutation?

Back

A permutation is an arrangement of items from a larger set where the order does matter.

Front

How do you calculate the number of permutations of n items taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!, where n is the total number of items and r is the number of items to arrange.

Front

How do you calculate the number of combinations of n items taken r at a time?

Back

The formula is C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to choose.

Front

What is the theoretical probability of an event?

Back

The theoretical probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

If a bag contains 3 red marbles, 2 blue marbles, and 4 green marbles, what is the probability of drawing a blue marble?

Back

The probability is 2/9.

Front

In how many ways can you arrange 5 books on a shelf?

Back

The number of arrangements is 5! = 120.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.

Front

If you have 10 students and want to select a president and a vice president, how many ways can you do this?

Back

There are P(10, 2) = 10! / (10 - 2)! = 90 ways.