There are 22 different candies such that 6 are lemon-flavored, 9 are vanilla-flavored and 7 are strawberry-flavored. Mr Bean chooses 5 candies randomly out of these 22. What is the probability that
(A) all the chosen candies are vanilla-flavored?
(B) the chosen candies are of more than one flavor?
(C) he chooses at least two stawberry-flavored candies?
數學題!!!!!!!!probability
2009-12-03 2:06 am
回答 (2)
2009-12-03 2:27 am
✔ 最佳答案
A)P(all the chosen candies are vanilla-flavored)= (9/22)(8/21)(7/20)(6/19)(5/18) or (9C5 / 22C5)
= 1 / 209
B)P(the chosen candies are of more than one flavor)
= 1 - P(all the chosen candies are lemon-flavored) - P(all are vanilla-flavored)
- P(all are strawberry_flavored)
= 1 - 6C5/22C5 - 1/209 - 7C5/22C5
= 1 - 1/4389 - 1/209 - 1/1254
= 2909 / 2926
C)P(he chooses at least two stawberry-flavored candies)
= 1 - P(no stawberry-flavored) - P(only one stawberry-flavored)
= 1 - P(All are lemon or vanilla_flavored) - P(only one stawberry-flavored)
= 1 - (6+9)C5 / 22C5 - (7C1)*(6+9)C4 / 22C5
= 1 - 3003/26334 - 9555/26334
= 13776/26334
= 328/627
2009-12-03 2:45 am
A)P(all the chosen candies are vanilla-flavored)
= (9/22)(8/21)(7/20)(6/19)(5/18) or (9C5 / 22C5)
= 1 / 209
B)P(the chosen candies are of more than one flavor)
= 1 - P(all the chosen candies are lemon-flavored) - P(all are vanilla-flavored)
- P(all are strawberry_flavored)
= 1 - 6C5/22C5 - 1/209 - 7C5/22C5
= 1 - 1/4389 - 1/209 - 1/1254
= 2909 / 2926
C)P(he chooses at least two stawberry-flavored candies)
= 1 - P(no stawberry-flavored) - P(only one stawberry-flavored)
= 1 - P(All are lemon or vanilla_flavored) - P(only one stawberry-flavored)
= 1 - (6+9)C5 / 22C5 - (7C1)*(6+9)C4 / 22C5
= 1 - 3003/26334 - 9555/26334
= 13776/26334
= 328/627
= (9/22)(8/21)(7/20)(6/19)(5/18) or (9C5 / 22C5)
= 1 / 209
B)P(the chosen candies are of more than one flavor)
= 1 - P(all the chosen candies are lemon-flavored) - P(all are vanilla-flavored)
- P(all are strawberry_flavored)
= 1 - 6C5/22C5 - 1/209 - 7C5/22C5
= 1 - 1/4389 - 1/209 - 1/1254
= 2909 / 2926
C)P(he chooses at least two stawberry-flavored candies)
= 1 - P(no stawberry-flavored) - P(only one stawberry-flavored)
= 1 - P(All are lemon or vanilla_flavored) - P(only one stawberry-flavored)
= 1 - (6+9)C5 / 22C5 - (7C1)*(6+9)C4 / 22C5
= 1 - 3003/26334 - 9555/26334
= 13776/26334
= 328/627
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