Exam Review 2

Front

What is a resultant vector?

Back

A resultant vector is the vector that results from adding two or more vectors together. It represents the combined effect of those vectors.

Front

How do you calculate the number of different outcomes in a race with prizes for the top three positions?

Back

Use the permutation formula: n! / (n - r)!, where n is the total number of participants and r is the number of positions. For 8 swimmers and 3 prizes, it's 8! / (8 - 3)! = 336.

Front

What is the probability of an event?

Back

Probability is a measure of the likelihood that an event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

How do you estimate the height of an object using a diagram?

Back

Use similar triangles or proportions based on the diagram to estimate the height. Measure the length of the shadow and the height of a reference object.

Front

What is expected value in probability?

Back

Expected value is the average amount you can expect to win or lose per bet if you were to repeat the experiment many times. It is calculated by multiplying each outcome by its probability and summing the results.

Front

Define a vector in mathematics.

Back

A vector is a quantity that has both magnitude and direction, often represented as an arrow in a coordinate system.

Front

What is the formula for calculating permutations?

Back

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

Front

What is the difference between combinations and permutations?

Back

Permutations consider the order of selection, while combinations do not. For example, choosing 2 out of 3 items (A, B, C) gives different results in permutations (AB, AC, BA, BC, CA, CB) than in combinations (AB, AC, BC).

Front

How do you find the probability of multiple independent events?

Back

Multiply the probabilities of each independent event. For example, if P(A) = 1/2 and P(B) = 1/3, then P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6.

Front

What is a sample space in probability?

Back

A sample space is the set of all possible outcomes of a probability experiment. For example, flipping a coin has a sample space of {Heads, Tails}.