12.7 - The Complement

Front

What is the complement of an event in probability?

Back

The complement of an event A is the event that A does not occur. It is denoted as A' or Ac, and the probability of the complement is given by P(A') = 1 - P(A).

Front

If the probability of an event occurring is 0.62, what is the probability of its complement?

Back

The probability of the complement is P(A') = 1 - P(A) = 1 - 0.62 = 0.38 or 38%.

Front

How do you calculate the probability of at least one event occurring when multiple independent events are involved?

Back

To find the probability of at least one event occurring, calculate the complement of the probability that none of the events occur.

Front

What is the formula for calculating the probability of independent events occurring together?

Back

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

Front

If two students are chosen at random and the probability that one has a car is 0.56, what is the probability that both have a car?

Back

P(both have a car) = P(A) * P(B) = 0.56 * 0.56 = 0.3136 or 31.4%.

Front

What is the probability of all three students carrying their lunch in a lulu bag if 42% do?

Back

P(all three carry lulu bags) = P(A) * P(B) * P(C) = 0.42 * 0.42 * 0.42 = 0.07408 or 7.4%.

Front

How do you find the probability of drawing a face card or a heart from a standard deck of cards?

Back

Calculate the probability of drawing a face card and the probability of drawing a heart, then subtract the probability of drawing a card that is both (face card that is also a heart).

Front

What is the total number of face cards in a standard deck of playing cards?

Back

There are 12 face cards in a standard deck (3 face cards in each of the 4 suits: King, Queen, Jack).

Front

How many hearts are in a standard deck of playing cards?

Back

There are 13 hearts in a standard deck of playing cards.

Front

What is the probability of drawing a heart from a standard deck of cards?

Back

The probability of drawing a heart is P(heart) = Number of hearts / Total number of cards = 13/52 = 0.25 or 25%.