Probability Flashcard

Front

What is the fundamental principle of counting in probability?

Back

The fundamental principle of counting states that if there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to do both.

Front

How do you calculate the number of combinations of choosing 'r' items from 'n' items?

Back

The number of combinations is calculated using the formula: C(n, r) = n! / (r!(n - r)!), where '!' denotes factorial.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, choosing A, B, C is different in permutations but the same in combinations.

Front

If a spinner has 12 equal sections, what is the probability of landing on a specific section?

Back

The probability of landing on a specific section is 1/12.

Front

What is the probability of rolling a sum of 7 with two six-sided dice?

Back

There are 6 combinations to roll a sum of 7 out of 36 total combinations, so the probability is 6/36 or 1/6.

Front

How do you find the probability of an event not occurring?

Back

The probability of an event not occurring is 1 minus the probability of the event occurring: P(not A) = 1 - P(A).

Front

What is a sample space in probability?

Back

A sample space is the set of all possible outcomes of a probability experiment.

Front

How do you calculate the total number of outcomes for multiple independent events?

Back

Multiply the number of outcomes for each event. For example, if Event A has 'm' outcomes and Event B has 'n' outcomes, the total outcomes are m × n.

Front

What is the formula for calculating the probability of the union of two events A and B?

Back

The probability of the union of two events is given by: P(A or B) = P(A) + P(B) - P(A and B).

Front

What is the expected value in probability?

Back

The expected value is the long-term average of a random variable, calculated as E(X) = Σ [x * P(x)], where x is an outcome and P(x) is its probability.