Question

Describe the complement of each event.

(a) My class has 27 students, 25 are right handed.

(b) Rolling a single 6-sided die and getting a result less than 3

Answer 1

Complement of an event - The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A. It is represented by A^{​​​​​​c}.

(a) My class has 27 students, 25 are right handed.

Let event A : students who are right handed

n(A) = 25

P(A) = 25/ 27

n(A^c) = n - n(A) = 27 - 25 = 2

P(A^c) = 1- P(A) = 2/27

(b) Rolling a single 6-sided die and getting a result less than 3

Rolling single six sided has 6 possible outcomes. Chances of getting selected out of (1,2,3,4,5,6) is equal.

Therefore

Sample space = {1,2,3,4,5,6}

Probability = 1/6.

Let event B : getting a result less than 3

It means only 1 or 2 can appear on die.possible outcomes are -

B = {1,2}

P(B) = 2/6

B^c :complement of event B

B^{​​​​​C} = getting result more than or equal to 3.

Possible outcomes are-

B^c = { 3,4,5,6}

P(B^c) = 4/6.

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