Use Boolean algebra to simplify the following logic gate circuit: :D₂ 노 A B C Output

Pleas help with these two questions.

Use R code: On Day 1, Basket A contains 10 red balls and Basket B contains 10 blue balls. Each morning you pick a ball at random from Basket A and put it in Basket B. Each evening, you pick a ball at random from Basket B and put it in Basket A. Every time you transfer a blue ball you drop a penny in a piggy bank, every time you transfer a red ball you drop a nickel in the piggy bank. On Day 366 morning, how many balls of each color are in the two baskets? On Day 366 morning how much money is in the piggy bank? The answers are not numbers, but random variables. Give their probability mass functions.

Determine the output for each of the following Boolean circuits. (please show work)

Section – A I Choose the correct answer: 1. pV(pA¬q) can be simplified to (a) ¬(pAq) (b) pAq (c) ¬(pVq) (d) pVq 2. If A = 1101 0 and B = 10110 are the two sets represented by bit string then A UB = (a) 01001 (b) 11010 (c) 00 100 (d) 10100

Your password in your company's ERP (Enterprise Resource Planning) System requires exactly eight characters. And each character is one of the of the 26 letters (a-z) or 10 integers (0-9). Let A denote the subset of passwords that begin with a vowel (either, a, e, i, o, u) and let B denote the subset of passwords that end with an even number (either 0,2,4,6, or 8) Suppose a hacker guessed that your password is in event A and B and selects a password at random from this subset. What is the probability that your password is hacked? O a. 1 O b. None among the choices O c. 1 368 5(367) O d. 1 (5) (5) (366)

Telephone area codes are three-digit numbers of the form XXX. Originally, the first and third digits were neither 0 nor 1 and the second digit was always a 0 or a 1. How many three-digit numbers of this type are possible?   Over time, the restrictions listed in part (a) have been altered; currently, the only requirement is that the first digit is neither 0 nor 1. How many three-digit numbers of this type are possible? Why were the original restrictions listed in part (a) altered?

At one point, license plates in a certain state consisted of 2 letters (excluding I, O, Q, and W), followed by 4 numbers. Complete parts (a) through (e) below. a) How many plates are possible when letters and numbers can repeat? Set up the expression that can be used to calculate the number of plates that are possible when letters and numbers can repeat. The expression is (Do not simplify.) The number of plates possible when letters and numbers can repeat is (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) b) How many plates would be possible if letters could repeat but numbers could not? (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) c) How many plates would be possible if letters could not repeat but numbers could? (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal…

Encrypt.

How many students enrolled in either Discrete Structure or Programming course if there are 201 students in Discrete Structure course, 130 students in Programming course and 88 students enrolled in both course? * O 419 O 159 O 155 O 243