Answer:
0.1667
Step-by-step explanation:
There are 6! ways to arrange the hats. The number of ways for which no guest will receive the proper hat is 5! (since there are 5 wrong hats for the first guest, 4 for the second guest, and so on). The probability that no guest will receive the proper hat is:
The probability is 0.1667.
The set X is convex.
In geometry, a subset of an affine space over the real numbers, or more broadly a subset of a Euclidean space, is said to be convex if it contains the entire line segment connecting any two points in the subset. A solid cube is an example of a convex set, whereas anything hollow or with an indent, such as a crescent shape, is not. Alternatively, a convex region is a subset that crosses every line into a single line segment.
b)The set X is convex as any two points on the set X is included in the whole set as x>0. So a line joining any two points on the set X is completely inside the set x.
c)set X is not a closed set as the compliment of the set is not an open set.
d)Set X is not bounded. If a set S contains both upper and lower bounds, it is said to be bounded. A set of real numbers is therefore said to be bounded if it fits inside a defined range. hence set x is not bounded.
To learn more about convex sets:
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