Eight draws are made at random with replacement from the box with numbers: 1,2,3,3,3. Find the probability of drawing exactly two 3's
Eight draws are made at random with replacement from the box with numbers: 1,2,3,3,3. Find the...
Draws are being made at random with replacement from a box. The number of draws is getting larger and larger. Say whether each of the following statements is true or false. a. The probability histogram for the sum of the draws ( when put in standard units) converges to the normal curve. b. The histogram for the numbers in the box when put in standard units converges to the normal curve. c. The histogram for the numbers drawn when you...
One hundred draws are made at random with replacement from the box: [1,1,2,3] The draws come out as follows: 45 1’s, 23 2’s, and 32 3’s. 1. the standard deviation of the sum of the draws is: 2. the standard deviation for the number of 1’s is:
Two draws are made at random without replacement from the digits {1,2,3,4}. Let X1 be the first digit drawn and X2 the second. Let M=max(X1,X2) and S=X1+X2. a) Find ?(?). b) Make a joint distribution table for M and S. c) Use the table in Part b to find the distribution of M. d) Find ?(?).
5. A box contains two $10 bills, five $5 bills, and eight $1 bills. Two bills are taken at random without replacement from the box. a. What is the probability of drawing exactly $15? b. What is the probability that both bills will be of the same denomination? (i.e., two $10, two $5, or two $1 bills are drawn)?
6 numbers are chosen in order from the numbers 1, 2, ..., 49 a. Find the probability the numbers are drawn in **strictly** increasing order; (i.e., the first < the second < the third) if i. draws are made without replacement ii. draws are made with replacement. b. Assume the draws are made without replacement. Find the probability that the numbers form an arithmetic sequence drawn in any possible order (for example 9,3,6,12,18,15) C.Assume the draws are made with replacement....
Problem 3. Consider a box with three blue and five red marbles. Suppose draws are made from the box with replacement until two red marbles are drawn. Let Y denote the number of draws required, and let X denote the number of draws it takes to obtain the first red marble. (1) Calculate P(X-s, Y t) for integers s and t, 1 3 (2) Use the above to find P(Y t). (3) Calculate P(X = sy-t) for 1 s <...
One hundred draws are made at random with replacement from 1, 2, 3, 4, 5. What is the chance of getting between 8 and 32 tickets marked 5?
A box contains two red balls and three green balls. Make a box model. Six draws are made with replacement from the box. Find the chance that: a) A red ball is never drawn. b) A green ball appears exactly three times. c) A green ball appears at least twice.
Problem #4: (10 points) In a state lottery, the player picks 6 numbers from a sequence of 1 through 51. At a lottery drawing, 6 balls are drawn at random from a box containing 51 balls, numbered 1 through 51. Find the following. (a) Probability the player matches exactly 5 numbers (b) Probability the player matches all 6 numbers (i.e. wins the lottery!) Problem #4: (10 points) In a state lottery, the player picks 6 numbers from a sequence of...
A box contains three cokes and two beers (root beer of course). Julie draws at random twice without replacement from the box. (Any draw is equally likely) a.) What is the probability that she gets at least one beer? b.) What is the probability that she drew a coke on the first draw given that she drew a beer on the second draw? Please explain step by step!