1. Compute the probability of having the sum of 10 by throwing (a) two dice, (b) three dice.

2. What is the probability of three of a kind for a poker hand with (a) a card deck of 52 cards, (b) a card deck of 32 cards by removing all cards of numbers deuce (2), three, four, five, and six?

3. Bernouli trial:

a. You throw a fair coin (p(Head) = ½)) 10 times, find the probability of at least 8 heads. List the formula, and also calculate the probability with 3 significant digits after the decimal point.

b. You throw 10 fair coins once, find the probability of at least 8 tails.

c. You throw a biased coin with p (Head) = 1/3, 5 times, find the probability of at least 3 heads.

d. You transmit a file of 200 bytes with BER (bit error rate) = 10-6, compute the probability of no bit error and also the probability of at most 1 bit error to 3 significant digits.

4. Classify for each case following if the two events X and Y are independent or not.

a. You throw a coin 3 times. X = {first throw = Head}, Y = {second throw = Tail}

b. You throw a coin 4 times, X = {there are at most 2 heads}, Y = {there are at least two tails}