Problem 1

What is the probability that a randomly number chosen from the set {1, 2, 3, 4, ..., 2020, 2021} satisfies NONE of the three following conditions?. Show details work

• It is a perfect cube
• It is a multiple of 11
• It is less than 600

Problem 2

A new investment bank has decided to invest TK45,000 on stocks, TK12,000 on mutual funds and the rest on bonds out of a total of TK60,000. It is predicting that 73%, 86% and 95% of its stocks, mutual funds and bonds respectively will increase in value after one year.Show details work

a) If a randomly selected asset increased in value after a year, what is the probability of it being a bond?

b) What is the probability of an asset not being a mutual fund if it did not increase in value after one year?

Problem 3

36 employees work in a company X. For a special purpose, the Chairperson of that company chose 8 employees' namesand kept his selection secret. The Deputy Director andthe General Manager also chose 4 and 5 employees respectively without letting each other know about their selections. (There might be common employees within DD's choices andGM's choices ). What is the probability that exactly 1 of DD's chosen employees and 2 of GM's chosen employees match the list of the Chairperson.Show details

Problem 4

Every season, participants of an elite marathon are shortlisted based on their last season rating. For runners rated Gold, Silver, and Bronze in the last season, the chances of getting selected are 82%, 73% and 58% respectively. If a runner is not selected, they are either put on a waiting list, or rejected. Unselected runners from all classes (Gold, Silver, and Bronze) are twice as likely to be put on the waiting list as being rejected. In the previous season, 12% of the runners were rated Gold, 26% were rated Silver, and the rest were rated Bronze. If a randomly chosen runner was put on the waiting list by four out of six independent selectors, what is the probability that they were rated Bronze? Show details