EOC Flashcard #4 A2B

Front

What is the definition of conditional probability?

Back

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

Front

How do you calculate the probability of an event?

Back

The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. P(A) = Number of favorable outcomes / Total outcomes.

Front

What is the formula for the probability of the union of two events?

Back

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

Front

How do you find the total number of combinations when selecting items?

Back

The total number of combinations can be calculated using the formula: 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 difference between permutations and combinations?

Back

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

Front

How do you calculate the total number of outfits from different clothing items?

Back

To find the total number of outfits, multiply the number of choices for each clothing item. For example, if there are 8 pants, 12 shirts, 15 ties, and 6 sport coats, the total outfits = 8 * 12 * 15 * 6.

Front

What is the probability of an event not occurring?

Back

The probability of an event not occurring is calculated as 1 minus the probability of the event occurring. If P(A) is the probability of event A, then P(A') = 1 - P(A).

Front

What is the definition of independent events in probability?

Back

Independent events are events where the occurrence of one event does not affect the occurrence of another. For independent events A and B, P(A ∩ B) = P(A) * P(B).

Front

How do you calculate the probability of selecting a specific color from a set of items?

Back

To calculate the probability of selecting a specific color, divide the number of items of that color by the total number of items. For example, P(blue) = Number of blue items / Total items.

Front

What is the formula for calculating the probability of selecting at least one event?

Back

The probability of selecting at least one event can be calculated using the complement rule: P(at least one) = 1 - P(none).