Discrete Probability : Coin Flips

Suppose three fair coins are flipped. Find the probability for each of the following events. 1. Exactly two coins are tails. 2. At most two coins are tails.

Dice Probability. This solution shows an intuitive method for finding the probability of an event when rolling a pair of dice.

Suppose a pair of dice are flipped. Find the probability for each of the following events: 1. The sum of the dots is even. 2. The sum of the dots is at least 5.

Discrete Probability 12b

A team has probability 2/3 of winning whenever it plays. Find the probability that the team will win at most 4 out of 5 games.

Discrete Probability

A baseball player's batting average is .250. Find the probability that he will get hits at least one hit in 4 times at bat.

Algebraic Properties 8b

Given the algebra , where f and g are unary operations and a is a constant of S, suppose that f(f(x)) = g(x) and g(g(x)) = x for all x ε S. Show that f(f(f(f(x)))) = x for all x ε S.

Binary Connectives 17

Show that there are no complete single binary connectives other than NAND and NOR. Hint: Let f be the truth function for a complete binary connective. Show that f(true,true)=false and f(false,false)=true because the negation operation must be represented in terms of f. Then consider the remaining cases in the truth table for f ...continues

Quadratic Residues

Please see the attached file for the fully formatted problems. Fix a positive integer a We say that a is a quadratic residue modulo n if there exists x such that a = x^2 mod n. (a) Let n be an odd prime and a be a non-zero quadratic residue modulo n. Show that there are exactly two values in{O.1....,n—1} satisfying x^2=amodn ...continues

Show W is true for any interpretation whose domain has 2 elements.

Please see the attached file for the fully formatted problem. 71. 14b. Given the wff .... Show that W is true for any interpretation whose domain has two elements.

What is dual of each of the following Boolean expressions?

What is dual of each of the following Boolean expressions? 7b. x(y+z) 7d. xy+z

Making a Boolean algebra into a Partially Ordered Set

11b. A boolean algebra can be made into a partially ordered set by letting a≤b mean a=b. Show that a≤b iff b= a + b