Topic 53 Geometric Probability

Front

What is geometric probability?

Back

Geometric probability is the probability that a point chosen at random from a geometric figure will fall within a specified region of that figure.

Front

How do you calculate the probability of a point falling in a shaded region?

Back

The probability is calculated by dividing the area of the shaded region by the total area of the figure.

Front

If a figure has a total area of 100 square units and a shaded area of 25 square units, what is the probability of randomly selecting a point in the shaded area?

Back

The probability is 25/100 = 0.25 or 25%.

Front

What is the formula for geometric probability?

Back

Geometric Probability = (Area of the favorable region) / (Total area of the figure).

Front

In a dartboard, if the area of the target region is 30 square units and the total area is 60 square units, what is the probability of hitting the target?

Back

The probability is 30/60 = 0.5 or 50%.

Front

What does it mean if the geometric probability is 0.75?

Back

It means there is a 75% chance that a randomly chosen point will fall within the specified region.

Front

If a marble falls randomly on a figure with a shaded area of 20 square units and a total area of 80 square units, what is the geometric probability?

Back

The geometric probability is 20/80 = 0.25 or 25%.

Front

What is the significance of the shaded area in geometric probability problems?

Back

The shaded area represents the favorable outcomes for the probability calculation.

Front

How can geometric probability be applied in real-life situations?

Back

Geometric probability can be used in various fields such as engineering, architecture, and game design to assess risks and outcomes.

Front

If a dartboard has a total area of 50 square units and a middle region area of 20 square units, what is the probability of hitting the middle region?

Back

The probability is 20/50 = 0.4 or 40%.