Five candidates ( A, B, C, D , and E) have a chance to be selected to be on American Idol . Any subset of them (including none of them or all of them) can be selected, and assume that the selection process is completely random (the subsets of candidates are all equally likely). Find the probability of each of the following events. ( Hint : Do Exercise 16 first.) a. E 1 : “two candidates get selected.” b. E 2 : “three candidates get selected.” c. E 3 : “three candidates get selected, and A is not one of them.”
Five candidates ( A, B, C, D , and E) have a chance to be selected to be on American Idol . Any subset of them (including none of them or all of them) can be selected, and assume that the selection process is completely random (the subsets of candidates are all equally likely). Find the probability of each of the following events. ( Hint : Do Exercise 16 first.) a. E 1 : “two candidates get selected.” b. E 2 : “three candidates get selected.” c. E 3 : “three candidates get selected, and A is not one of them.”
Solution Summary: The author calculates the probability of an event E_1 in which two candidates get selected.
Five candidates (A, B, C, D, and E) have a chance to be selected to be on American Idol. Any subset of them (including none of them or all of them) can be selected, and assume that the selection process is completely random (the subsets of candidates are all equally likely). Find the probability of each of the following events. (Hint: Do Exercise 16 first.)
a.
E
1
: “two candidates get selected.”
b.
E
2
: “three candidates get selected.”
c.
E
3
: “three candidates get selected, and A is not one of them.”
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