GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY.

Hi,kindly reply with whole answers correct,accurate answers and step by step working.Do not skip step.Be very clear and mention about the formula for each step.Make sure the answers are correct and accurate. Be very organised with the working and systematic.Please explain to support and make it clear. Please number the answers according to each part,part 1 and part 2

STA EXERCISES

PART 1

PROBABILITY 1. The probability that a certain type of machine will break down in the first month of operation is 0.1. Three machine of this type are installed at the same time. The performances of the three machines are independent. Find the probability that at the end of the first month. a. All three machines have broken down b. Just one machine has broken down c. At least one machine is working 2. Data about employment for males and females in a small rural area are shown in the table below. Unemployed Employed Male 206 412 Female 358 305 A person from this area is chosen at random. Let M be the event that the person is male and let E be the event that the person is employed. a. Find P(M) b. Find P(M and E) c. Are M and E independent events? Justify your answer. d. Given that the person chosen is unemployed, find the probability that the person is female. 3. Event A and B are such that P(A)=0.3,P(B)=0.6 and P(A or B)= 0.72.State,giving a reason in each case .whether events A and B are a. Mutually exclusive b. Independent 4. The probability that Arif goes swimming on any day is 0.2. On a day that he goes swimming, the probability that Arif has burgers for supper is 0.75.On a day when he goes not to swimming, the probability that he has burgers for his supper is x. a. Draw a tree diagram based on above case study b. The probability that Arif has burgers for supper on any day is 0.5 1. Find x ii. Given that Arif has burgers for supper, find the probability that he went swimming that day.PROBABILITY DENSTIY FUNCTION: DISCRETE RANDOM VARIABLES 1. Emma is playing a game with a biased five sided spinner marked with the numbers 1,2,3,4, and 5. When she spins the spinner, her score, is the number on which the spinner lands. The probability distribution of X is shown in the table: X 1 2 3 4 5 P(X-x) 0.15 0.24 0.25 0.19 a) Find the value of a. b) Find the probability that the score is at least 4 c) Find the probability that the score is less than 5 d) Find P(2