Suppose n balls are thrown into n labeled bins one at a time, where n is a positive even integer. (a) what is the probability that exactly k balls land in the first bin, where k is an integer 0 ≤ k ≤ n? (b) what is the probability p that at least half of the balls land in the first bin? (you may leave your answer as a summation.) (c) using the union bound, give a simple upper bound, in terms of p, on the probability that some bin contains at least half of the balls. (d) what is the probability, in terms of p, that at least half of the balls land in the first bin, or at least half of the balls land in the second bin?

step-by-step explanation:

20% of 120 is 24. if you subtract 24 from 120 you get 96

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc