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

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

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) =
`(1)/(6)`

∵ P(A) + P(A') = 1

∴
`(1)/(6)` + P(A') = 1

- Subtract
`(1)/(6)` from both sides

∴ P(A') =
`(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