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, denoted as A'. The probability of the complement is given by P(A') = 1 - P(A).

Front

If the probability of an event occurring is 62%, what is the probability of it not occurring?

Back

The probability of the event not occurring is 1 - 0.62 = 0.38 or 38%.

Front

How do you calculate the probability that at least one of two independent events does not occur?

Back

To find the probability that at least one of two independent events does not occur, first calculate the probability that both events occur, then subtract that from 1: P(at least one does not occur) = 1 - P(both occur).

Front

In a survey, if 38% of students have a study hall, what is the probability that both selected students do not have a study hall?

Back

If 38% have a study hall, then 62% do not. The probability that both do not have a study hall is 0.62 * 0.62 = 0.3844 or 38.44%.

Front

What is the formula for finding the probability of drawing two specific cards from a deck without replacement?

Back

The probability of drawing two specific cards without replacement is P(A) = (number of favorable outcomes for first card / total cards) * (number of favorable outcomes for second card / total remaining cards).

Front

How do you find the probability of drawing a heart and another heart from a standard deck of cards?

Back

The probability of drawing a heart first is 13/52. If the first card is a heart, the probability of drawing another heart is 12/51. Thus, P(drawing two hearts) = (13/52) * (12/51).

Front

What is the area of a rectangle with dimensions 5 by 11?

Back

The area of a rectangle is calculated by multiplying its length by its width. Area = 5 * 11 = 55 square units.

Front

How do you calculate the area of a circle with a radius of 3?

Back

The area of a circle is calculated using the formula A = πr². For a radius of 3, A = π(3)² = 9π, approximately 28.3 square units.

Front

What is the probability of a point being in a shaded region of a rectangle if the area of the shaded region is known?

Back

The probability of a point being in the shaded region is calculated as P = (Area of shaded region) / (Total area of rectangle).

Front

If the total area of a rectangle is 55 square units and the area of the shaded region is 28.3 square units, what is the probability of selecting a point in the shaded region?

Back

P = 28.3 / 55 = 0.515 or 51.5%.