Complement of an Event The complement of an event E is the set of all outcomes n

Question

Complement of an Event The complement of an event E is the set of all outcomes not in E. Thus, the complement o represents the event that E does not occur. Union of Events The union of the events E and F is the set of all outcomes in E or F (or both). Thus E UF the event that E occurs or F occurs (or both). Intersection of Events The intersection of the events E and F is the set of all outcomes common to E and F. Thus represents the event that both E and F occur. Mutually Exclusive Events If E and F are events, then E and F are said to be disjoint or mutually exclusive if E n F (Hence, they have no outcomes in common.) Problem 1. Describe the sample space S of the experiment and list the elements of the a) Three coins are tossed; the result is at most one head. b) Two distinguishable dice are rolled; the numbers add to 7 ) Two indistinguishable dice are rolled; both numbers are prime.

Explanation / Answer

a) At most 1 head means Maximum 1 head. So we can have 1 head or heads.

HTT, THT, TTH, TTT

b) Number add to 7. (1,6) - (6,1) - (5,2) - (2,5) - (4,3) - (3,4)

c) The prime numbers in both the dice are, 2,3 and 5

(2,2) - (2,3) - (2,5) - (3,2) - (3,3) - (3,4)- (5,2) - (5,3) - (5,4)

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