Question

RECREATION A parachutist is aiming to land in a circular target with a 10-yard radius. The target is in a rectangular field that is 120 yards long and 30 yards wide. Given that the parachutist will land in the field, what is the probability he will land in the target?

Answer 1

The probability that the parachutist will land in the target is found by dividing the area of the circular target by the area of the rectangular field, resulting in approximately 0.0873 or 8.73%.

Step-by-step explanation:

To calculate the probability that the parachutist will land in the target, we need to compare the area of the circular target to the area of the rectangular field. The formula for the area of a circle is A = πr2, where r is the radius, and the formula for the area of a rectangle is A = length × width.

The area of the target, which is circular and has a radius of 10 yards, is

Atarget = π(10 yards)2

= 100π yards2. The area of the rectangular field is

Afield = 120 yards × 30 yards

= 3600 yards2.

Therefore, the probability of landing in the target can be calculated by dividing the area of the target by the area of the field:

P(target) = Atarget/Afield
= (100π yards2) / (3600 yards2)
= π/36 ≈ 0.0873

So, the probability that the parachutist will land in the target is approximately 0.0873, or 8.73%.