Probability

2011-03-31 6:37 am

1. Alex and Branda are 2 of the 40 students in a class. If 2 students are chosen at random as class representatives,find the probability that only one of them is chosen.2.Four digits are selected at random from (1,2,3,5,6,7,8,9) and arranged to form a 4-digit number. Find the probability that the number formed is a. an even numberb.greater than 8000

更新1:

雖然些字密密麻麻,但其實係2題來的 1. Alex and Branda ......... 2.Four digits............

回答 (1)

用戶2053

2011-03-31 7:04 am

✔ 最佳答案

1)P(only one of them is chosen)= 1 - P(All of them are chosen) - P(None of them are chosen)= 1 - (2/40)(1/39) - (38/40)(37/39)= 19/195Alternatively :(2C1) [(40-2)C1] / 40C2= 19/195
2a)The number of 4-digit even number
=
The number of ???2 (??? are choose from 1356789)
+
The number of ???6 (??? are choose from 1235789)
+
The number of ???8 (??? are choose from 1235679)= 3 * 7P3 = 630 's 4-digit even numberP(even)= 630 / 8P4
= 3/8Alternatively :Consider the last digit , 2 , 6 , 8 are even otherwise is oddSo P(E) = 3/82b)Consider the first digit must be 8 or 9 , P(>8000) = 2/8 = 1/4

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