1.A committee of 2 is selected from a group consisting of 5 people; John, Jake, Angel, Dexter and Aiza. Write the following events as sets, listing the outcomes they contain:

a.The sample space

b.Both members on the committee are male

c.Exactly one member is a male

2.Consider an experiment of tossing a pair of dice. Let the outcome be represented by an ordered pair, where the first component is the number on the first die and the second component is the number on the other die.List the following:

a.The sample space S

b.The event A that has number 3 comes up on either die.

c.The event B that the sum of two numbers is less than 8.

d.The event C that the two numbers is the same.

e.The event A B.

f.The event B C.

3.Of 120 students, 60 are studying Mathematics, 50 are studyingFilipino, and 20 are studying Mathematics and Filipino. If a student is chosen at random, find the probability that the student (a) is studying Mathematics or Filipino

(b) is studying neither Mathematics nor Filipino.

4.In a battle involving 100 men, all suffered injuries on any of the three parts of their bodies: head, arm, and leg. Of these, 42 men injured their heads, 43 men injured their arms, and 32 men injured their legs. Five men injured both their heads and arms, 8 men injured both their arms and legs and 6 men injured in both their heads and legs. If one man is chosen at random, find the probability that he is injured

a.in all the three parts of the body

b.in his head only

c.either in his arms or legs but not in his head

5.Compute the probability that when 3 cards are randomly drawn from a deck of ordinary playing cards, the ace and the king of the same suit are included in the selection.