a)Twelve people are selected randomly from a group of 50 to serve in a trial jury. Suppose Tim and Jane are two people in the pool of 50 people. What is the probability that both Tim and Jane will serve on the jury.
b) A fair six- sided die is tossed 10 times and the resulting sequence is recorded. Let E be the event that the sequence of 10 outcomes contains exactly 4 ones, and let G be the event that the sequence of 10 outcomes contains exactly 6 threes. E and G can occur simultaneously.
c) Cards numbered 1-13 are well shuffled and 5 cards are drawn and placed in a row from right to left. What is the probability that all 5 cards are odd numbered.
d) A fair coin is tossed, a fair six-sided die is tossed, and three cards are drawn one at a time and without replacement from a standard 52 card poker deck. What is the probability that a 4 is tossed and three red cards are drawn.