Given A = {2, 5, 7} and B = {4, 5}, find B × A. O {(2, 4), (2, 5), (5, 4), (5, 5), (7, 4), (7, 5)} O{(4, 2), (4, 5), (4, 7), (5, 2), (5, 5), (5, 7)} O{(2, 4), (5, 4), (7,4)} ○ {(4, 2), (4, 5), (4, 7), (5, 5), (5, 7)}

Find the union: (7, 8, 9, 10, 11} U {6, 8, 10, 12}.

let A = {0, 75, 6, -42, 1088, 475, 609, 80, 195, 475} B = {98, -42, 1, 56, 82, 607, 741, 87, -475, 80} C= {0, 475, 485, 87, 9, -412, 90, 651, 584, 89} D = {80, -78, -452, -475, 56, 90, 431, -80, 7820} E = {1088, 4571, -80, -475, 324, 543, 777, 782} 1. Compute (a) A U B D)ט - C4 (e) (i) C – E (b) BUC (f) D – B () (An B) – C (c) An C (g)U – E (d) Bn D (h) E O B 2. Compute (a) AUD (e) (C U E) – (A U C) (i) C O D (b) BUD () В - С 6) (An B) – (D n C) (c) Cn D (g) U – B (d) An D (h) C – B 3. Compute (a) A U BUC (d) (A U B) n C (g) E - A (b) An BnC (e) (U – A) U (U – B) (h) A - E (c) An (B U C) () (U – A) n (U – B) 4. Compute (a) (A – C) n (C – D) (c) BUB (e) (U – E) U (U - D) (g) E – B (b) AU U (d) Cn{ } () (U – C) n (U – E) (h) B - E

Elena is answering a matching practice problem where she has to match each of 4 items in a left column (A, B, C, D) to 4 items on the right (1, 2, 3, 4) so th each item is used exactly once. For example one way to answer this problem is A4, B2, C1, D3. 1. What are all the possible ways she could answer this problem? 2. The actual solution is A1, B2, C3, D4. If Elena was equally likely to guess any answer, use the sample space to find: 1. The probability of getting exactly O items matched correctly. 2. The probability of getting exactly 1 item matched correctly. 3. The probability of getting exactly 2 items matched correctly. 4. The probability of getting exactly 3 items matched correctly. 5. The probability of getting exactly 4 items matched correctly.

The game of American Roulette consists of spinning a wheel in one direction and then spinning a small ball in the other direction, see videoOpens externally [+]. The ball will eventually fall into a slot of the wheel. The wheel is divided into 38 slots. There are 36 slots numbered from 1 through 36 and 2 slots which are labeled with zero "0" and double zero "00". The zero and double zero are colored green, 18 slots are colored red, and the other 18 are colored black. See the below picture.A common bet in the game is to bet on red or black which pays even money. For example, if you bet a $1.00 on red and the ball falls into a red slot, then you win $1.00. Otherwise, you lose $1.00. Suppose you play the game and you bet $6 on red. Let X = the amount you win.a.) Complete the probability distribution table. (Write answers as fractions.) X P(X) -6    6    b.) Find the expected value (mean) of X.μμ =    (Write you answer as fraction or round to two decimal places.)c.) Find the…

An experiment is designed to see whether 3rd graders can write faster with a pen or pencil. Four third graders participate, 2 boys and 2 girls. For each child, a marble is drawn without replacement from a bucket containing 2 red marbles and 2 blue marbles. If a red marble is selected, the child gets a pen and if blue, the child gets a pencil. The children are assigned in this order: boy 1, girl 1, boy 2, girl 2. LetX be the number of boys assigned to a pen. Find E (X). Find SD(X). а. b.

Find the number of arrangements of the digits {0,1,2,3,4,5,6,7,8,9} such that the first digit is less than 7 AND the second digit is greater than or equal to 2.

Why did you pick (a,b) to be (1,1)? Can anything be chosen instead of  (1,1)?                                           91,1)?

A box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. Assume the plain donuts are identical, and the chocolate donuts are identical. How many visually distinct arrangements of the donuts are there?

A monkey has filled in a 3 × 3 grid with the numbers 1, 2, . . . , 9. A cat writes down thethree numbers obtained by multiplying the numbers in each horizontal row. A dog writesdown the three numbers obtained by multiplying the numbers in each vertical column.Can the monkey fill in the grid in such a way that the cat and dog obtain the same listsof three numbers? What if the monkey writes the numbers 1, 2, . . . , 25 in a 5×5 grid? Or1, 2, . . . , 121 in a 11 × 11 grid? Can you find any conditions on n that guarantee that itis possible or any conditions that guarantee that it is impossible for the monkey to writethe numbers 1, 2, . . . , n^2 in an n × n grid so that the cat and the dog obtain the same lists of numbers? Please provide a mathematically rigorous solution with proofs that could be understood by a person at a high school level.