7.5 Topic 5: Probability 39. A family wants to have two children. The children can either be male or female. What is the sample space for this experiment? (The order in which the couple has children does matter to the parents.) 40. Let the sample space S of a random experiment be the numbers 1 through 10. So, S = {1,2, 3, 4, 5, 6, 7,8, 9, 10}. Define events A, B, and C as follows. A: {1,2,3,5,6,7,8,9} B: { 2,4,5,7,9 } {1,2,3,4,5} C: (a) What outcomes are in the event AN B? (b) What outcomes are in the event BUC? (c) What outcomes are in the event C'? (d) Are the events An B and BnA the same? Why? (e) Are the events BUC and CUB the same? Why? 41. A survey of 100 male students and 100 female students regarding their favorite Mexican food restaurant yielded the results given below. Gender Chipotle Moe's Salsaritas Qʻdoba Male 20 35 38 17 13 Female 30 40 dadeng (a) What is the probability that a respondent is male? (b) What is the probability that a respondent likes Q'doba? (c) What is the probability that a respondent likes Salsaritas and is female? (d) What is the probability that a respondent likes Salsaritas or is female? 42. Consider two disjoint (or mutually exclusive) events A and B. If P(A) = 0.7 and P(B) = 0.2, find P(AUB). %3D %3D 43. Consider two disjoint (or mutually exclusive) events A and B with P(A) = 0.7 and P(B) = 0.4. Are these probabilities correctly assigned? (Hint: Calculate P(AUB).) %3D %3D 44. Suppose P(A) = 0.60 and P(B) = 0.7. Can events A, B be disjoint? %3D %3D 45. It is estimated that 63% of Americans will watch the Masters golf tournament and only 48% will watch the British Open. If it is estimated that 37% of Americans will watch both tournaments, what is the probability that they will watch at least one of the golf tournaments? 46. Consider drawing two cards from a regular deck of cards (52 cards total, 4 suits, 13 cards in each suit). What is the probability that you draw two Aces if the cards are drawn (a) With replacement? (b) Without replacement?

Q: could you clarify part a please ? is that a g? or a 9? what is part a answer??

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A: →A∪B : Set of elements present in either A or B.→A∩B : Set of elements present in both A and B.

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.