Question

Given the event​ "a die lands with a 6 on​ top", which of the following is the complement of this​ event? Choose the correct answer below.
A. The number of times the die lands with a 6 on top in n throws of the die
B. The die lands with a 3 on the top
C. The die lands with a 6 on the bottom
D. The die lands with a​ 1, 2,​ 3, 4, or 5 on top

Answer 1

Answer:

The die lands with a​ 1, 2,​ 3, 4, or 5 on top ⇒ answer D

Step-by-step explanation:

- Complementary events are two outcomes of an event that are the

 only two possible outcomes

- The Complement Rule states that the sum of the probabilities of

  an event and its complement must equal 1

- P(A) + P(A') = 1

- Lets solve the problem

- The event A is:

  " a die lands with a 6 on​ top "

∴ P(A) = $\frac{1}{6}$

∵ P(A) + P(A') = 1

∴ $\frac{1}{6}$ + P(A') = 1

- Subtract $\frac{1}{6}$ from both sides

∴ P(A') = $\frac{5}{6}$

∵ The die has six numbers from 1 to 6

∴ The other numbers than 6 are 1 , 2 , 3 , 4 and 5

∴ The complement of event A is:

   " A die lands with 1 , 2 , 3 , 4 or 5 "

* The complement of the event is:

 The die lands with a​ 1, 2,​ 3, 4, or 5 on top