Pre-Calculus Final: Probability and combinatorics

Front

What is the general multiplication rule in probability?

Back

The general multiplication rule states that the probability of two events A and B occurring together is given by P(A and B) = P(A) * P(B|A), where P(B|A) is the conditional probability of B given A.

Front

How do you calculate the probability of drawing a red card or a king from a standard deck of 52 cards?

Back

To find the probability of drawing a red card or a king, use the formula: P(A or B) = P(A) + P(B) - P(A and B). There are 26 red cards and 4 kings, but 2 of the kings are red. Thus, P(red or king) = 26/52 + 4/52 - 2/52 = 28/52 = 7/13.

Front

What is the formula for calculating the probability of either event A or event B occurring?

Back

The formula is P(A or B) = P(A) + P(B) - P(A and B). This accounts for the overlap between the two events.

Front

How many ways can a committee of 3 be selected from a group of 10 people?

Back

The number of ways to choose a committee of 3 from 10 is calculated using combinations: C(n, r) = n! / (r!(n-r)!), where n is the total number of people and r is the number of people to choose. Thus, C(10, 3) = 10! / (3!(10-3)!) = 120.

Front

What is the probability of selecting a committee of 3 people from a group of 10, where the order does not matter?

Back

The probability is calculated as the number of successful outcomes over the total outcomes. If selecting 3 from 10, the total ways to choose is C(10, 3) = 120. If we consider one specific committee, the probability is 1/120.

Front

Define conditional probability.

Back

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(B|A), which is the probability of B given A.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not. For example, selecting 3 people from a group of 5 can be done in different orders (permutations) or just as a group (combinations).

Front

How do you calculate the probability of independent events?

Back

For independent events A and B, the probability of both events occurring is P(A and B) = P(A) * P(B).

Front

What is a Venn diagram and how is it used in probability?

Back

A Venn diagram is a visual representation of sets and their relationships. In probability, it helps to illustrate the probabilities of events and their intersections.

Front

What is the probability of drawing a specific card from a standard deck?

Back

The probability of drawing a specific card from a standard deck of 52 cards is 1/52, since there is only one of each card.