DRAWING CARDS AND TOSSING COINS
TYPES OF EVENTS
Joint or Mutually Inclusive / Disjoint or Mutually Exclusive Two events A and B have a common intersection
In the Venn Diagram, the subsets A and B intersect. / / Two events A and B have no common intersection
In the Venn Diagram, the subsets A and B are separate. /
In Probability, a common experiment is drawing a card from a deck. The sample space has 52 possible outcomes.
Task4:
For #31-34, a playing card is drawn from a deck. Draw a Venn diagram for each pair of events, find each probability and
circle whether the pair of events are mutually inclusive or exclusive.
31. /These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event F: The card is a face card.
Event H: The card is hearts . / P(F) or the probability that the card is a face card. / P(H) or the probability that the card is hearts .
(iii) / (iv) / (v) / (vi)
P(~F) or the probability that the card is NOT a face card. / P(~H) or the probability that the card is NOThearts . / P(FH) or the probability that the card is a face cardANDthe card is hearts . / P(FH) or the probability that the card is a face cardORthe card is hearts .
32. /
These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event L: The card is a letter card.
Event N: The card is a number card. / P(L) or the probability that the card is a letter card. / P(N) or the probability that the card is a number card.
(iii) / (iv) / (v) / (vi)
P(~L) or the probability that the card is NOT a letter card. / P(~N) or the probability that the card is NOTa number card. / P(LN) or the probability that the card is a letter cardANDthe card is a number card. / P(LH) or the probability that the card is a letter cardORthe card is a number card.
33. /
These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event A: The card has a number less than 8.
Event B: The card has a number more than 3. / P(A) or the probability that the card has a number less than 8. / P(B) or the probability that the card has a number more than 3.
(iii) / (iv) / (v) / (vi)
P(~A) or the probability that the card does NOT have a number less than 8. / P(~B) or the probability that the card does NOT have a number more than 3. / P(AB) or the probability that the card has a number less than 8 AND more than 3. / P(AB) or the probability that the card has a number less than 8 OR more than 3.
34. /
These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event A: The card has a number less than 5.
Event B: The card has a number more than 6. / P(A) or the probability that the card has a number less than 5. / P(B) or the probability that the card has a number more than 6.
(iii) / (iv) / (v) / (vi)
P(~A) or the probability that the card does NOT have a number less than 5. / P(~B) or the probability that the card does NOT have a number more than 6. / P(AB) or the probability that the card has a number less than 5AND more than 6. / P(AB) or the probability that the card has a number less than 5OR more than 6.
In Probability, a common experiment is tossing a coin where the result can be heads (H) or tails (T).
Suppose one is tossed four times. Then, the sample space has 16 possible outcomes.
Task5:
For #35-38, a coin is tossed four times. Draw a Venn diagram for each pair of events, find each probability and
circle whether the pair of events are mutually inclusive or exclusive.
35. /These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event A: The tosses have two heads.
Event B: The tosses have a tail. / P(A) or the probability that the tosses have two heads. / P(B) or the probability that the tosses have a tail.
(iii) / (iv) / (v) / (vi)
P(~A) or the probability that the tosses does NOThave two heads. / P(~B) or the probability that the tosses does NOT have a tail. / P(AB) or the probability that the tosses have two heads AND one tail. / P(AB) or the probability that the tosses have two headsORone tail.
36. /
These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event A: The tosses have exactly three heads
Event B: The tosses have exactly two tails. / P(A) or the probability that the tosses have exactly three heads. / P(B) or the probability that the tosses have exactly two tails.
(iii) / (iv) / (v) / (vi)
P(~A) or the probability that the tosses does NOT have exactly three heads. / P(~B) or the probability that the tosses does NOT have exactly two tails. / P(AB) or the probability that the tosses have exactly three headsANDexactly two tails. / P(AB) or the probability that the tosses have exactly three headsORexactly two tails.
37. /
These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event A: The tosses have at least three heads.
Event B: The tosses have at least one tail. / P(A) or the probability that the tosses have at least three heads. / P(B) or the probability that the tosses have at least one tail.
(iii) / (iv) / (v) / (vi)
P(~A) or the probability that the tosses does NOT have at least three heads. / P(~B) or the probability that the tosses does NOT have at least one tail. / P(AB) or the probability that the tosses have at least three heads AND at least one tail. / P(AB) or the probability that the tosses have at least three heads OR at least one tail.
38. /
These events are mutually
{ inclusive, exclusive } / (i) / (ii)
Event A: The tosses have at least two heads.
Event B: The tosses have at least three tails. / P(A) or the probability that the tosses have at least two heads. / P(B) or the probability that the tosses have at least three tails.
(iii) / (iv) / (v) / (vi)
P(~A) or the probability that the tosses does NOT have at least two heads. / P(~B) or the probability that the tosses does NOT have at least three tails. / P(AB) or the probability that the tosses have at least two heads AND at least three tails. / P(AB) or the probability that the tosses have at least two heads OR at least three tails.