Question

8. Find the probability of winning a lottery with the following rule. Select the six winning numbers from​ 1, 2, . . .​ , 37. ​

(In any order. No​ repeats.)

​P(winning)=____

​(Type an integer or a simplified​ fraction.)

9. In designing an experiment involving a treatment applied to 3 test​ subjects, researchers plan to use a simple random sample of 3 subjects selected from a pool of 57 available subjects.​ (Recall that with a simple random​ sample, all samples of the same size have the same chance of being​ selected.) Answer the questions below.

a. How many different simple random samples are​ possible?____

B. What is the probability of each simple random sample in this​ case?____

10. When nine basketball players are about to have a​ free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical​ order? Assume each player has a different name.

​P(shoot free throws in alphabetical ​order)=___

​(Type an integer or a simplified​ fraction.)

Answer 1

Ans.

(8). Totalnumber of lottery = 37, numbered from 1 to 37

Winning number = 6, i.e. only one winning number out of 37

P(winning) = 1/37 = 0.027

9.(a). Population size, N = 57

and the sample size, n = 3

The total number of samples for

(I). Without replacement $=\binom{57}{3} = 29260$

(II). With replacement = 57³ = 185193

(b). If the simple random sample is drawn by without replacement then the probability of each sample is = 1/ 29260

(10).

P(shoot free throws in alphabetical order ) = 1/9! = 1/362880