The City Transit Authority plans to hire 6 new bus drivers. From a group of 100 qualified applicants, of whom?
a) P(Mary selected) = 6 / 100 since they are drawing 6 names and there are 100 candidates Or P(not Mary) = 99/100 * 98/99 * 97/98 * 96/97 * 95/96 * 94/95 (those are the chances that someone else's name will be picked on each of 6 successive drawings, without replacement) Everything cancels except 94 / 100 and 1 - 94/100 = 6/100 = 0.06 a, part 2) P(John and Mary) = 98 c 4 / 100 c 6 = 0.00303030303 or 0.0030 = 3/1000 rounded. since that is how many ways to pick John and Mary (1 way) * number of ways to fill the other 4 spots from the other 98 candidates. b) P(Mary) = 3 / 40 = 0.075 since in there are 3 spots and 40 candidates. Or P(not Mary) = 39/40 * 38/39 * 37/38 = 37/40 and 1 - 37/40 = 3/40 b, part 2) P(Mary) = 3/40 P(John) = 3/60 P(both) = 9/2400 = 0.00375 = 0.0038 rounded
The City Transit Authority plans to hire 12 new bus drivers from a group of 80 qualified applicants of which?
50 are men and 30 are women, 12 names are to be selected by lot. Supposed amy and rick are among the 80 qualified applicants. What is the probability that Mary's name will be selected?
Properties of Probability of an Event?
The City Transit Authority plans to hire 14 new bus drivers. From a group of 100 qualified applicants, of whom 65 are men and 35 are women, 14 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants. (a) What is the probability that Mary's name will be selected? What is the probability that both Mary's and John's names will be selected? (Round your answer to four decimal places.) (b) If it is stipulated that an equal number of men and women are to be selected (7 men from the group of 65 men and 7 women from the group of 35 women), what is the probability that Mary's name will be selected? (Round your answer to four decimal places.) What is the probability that Mary's and John's names will be selected? (Round your answer to four decimal places.)
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The City Transit Authority plans to hire 14 new bus drivers. From a group of 100 qualified applicants, of whom 55 are men and 45 are women, 14 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants. (b) If it is stipulated that an equal number of men and women are to be selected (7 men from the group on 55 men and 7 women from the group of 45 women), what is the probability that Mary's name will be selected? What is the probability that Mary's and John's names will be selected?
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The City Transit Authority plans to hire 16 new bus drivers. From a group of 100 qualified applicants, of whom 65 are men and 35 are women, 16 names are to be selected by lot. Suppose that Mary and John Lewis are among the 100 qualified applicants. (a) What is the probability that Mary's name will be selected? What is the probability that both Mary's and John's names will be selected? (Round your answer to four decimal places.) (b) If it is stipulated that an equal number of men and women are to be selected (8 men from the group of 65 men and 8 women from the group of 35 women), what is the probability that Mary's name will be selected? (Round your answer to four decimal places.) What is the probability that Mary's and John's names will be selected? (Round your answer to four decimal places.)