Question

A bullet is shot to a target which is a circle with radius of 20 meter. If the bullet assumed hit the circle and the probabilty of it to hit all points in the circle is the same. What is the probability of the bullet to hit the target IF:

a) at distance 4 meter from the center of the circle
b) at the distance of 4 meter fro the circumference of the circle
c) at the area of rectangle with each distances is 2 meter
d) from the center of the circle to the west and east
e) from the center of the circle to the south and north
f) at the distance 2 meter from the center of the circle at least 2 times from 10 times try

PLEASE ANSWER ALL OF THE QUESTION. I have a hard time understanding this subject.

Answer 1

Since every point in the circle has the same probability of getting hit therefore we can just take the ratio of the area for finding the probability.

P( hitting at a distance from 4 cm from the center) = = 0.04

P( hitting at a distance from 4 cm from the circumference) = = 0.36

P( at the area of the rectangle with each distance is 2 meter ),

for this case you know that the length of the rectangle is (2 + 2) = 4m and breadth will be 2 *sqrt ( 20^2 - 2^2) = 39.79

Area of rectangle = 4*39.79 = 159.16

Thus, P( at the area of the rectangle with each distance is 2 meter ) = 159.16/400 = 0.3979

Last Question,

This will become a binomial distribution because every independent hit is a brnoulli distribution with probability of success equal to

If X is the number of successful hits, X follows a binomial distribution

P( X > 1 ) = 1- P ( X=0) - P(X=1) = 0.00427