Kindly Answer the Following below. Kindly include solutions. Thanks!

Construct a probability distribution for the data and draw a histogram for the following: a. The probabilities that a patient will have 0_1 2 , or 3 medical tests performed on entering a hospital are 6/15, 5/15, 3/15, and 1/15 respectively. X P(X) b. A die is loaded in such a way that the probabilities of getting 1, 2, 3, 4, 5, and 6 are 1/2, 1/6, 1/12, 1/12, 1/12, and 1/12 respectively. X P(X) C. A box contains 3 P20 bills, 2 P50 bills, 1 P100 bill, and 1 P200 bill. X P(X) d. A family has three children. Let X represent the number of boys. X P(X) In each problem, which variable have the highest probability? Which variable has the lowest frequency? Ill. Complete the experiment by providing following information. a) Finding all possible outcomes using TREE DIAGRAM. 3 b) Listing all the possible outcomes in SAMPLE SPACE. 2 c) Counting the number of the variable in each outcome by making a TABLE. 3 d) Constructing a FREQUENCY DISTRIBUTION for the values of the random variables. 3 e) Constructing a PROBABILITY DISTRIBUTION for the values of the random variables. 3 () Represent the random variables using HISTOGRAM. 1 A basket contains 6 red apples and 4 green apples. If three (3) apples are taken from the basket one after the other, determine the possible values of the random variable R representing the number of red apple