Question

What is the probability of the complement of rolling a number less than 5 by using a six-sided die?

1/6
1/3
2/5
2/3

Answer 1

1/3

Explanation:

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Answer 2

Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:

1/3

Explanation:

Let A denote the event of rolling a number less than 5 in a six-sided die.

Now, we know that the Total outcomes are: 6

since, the sample space is given as: {1,2,3,4,5,6}

Also Number of favorable outcomes are: 4

since the numbers which are less than 5 are {1,2,3,4}

Now we have to find:

`P(A^c)`

where P denotes the probability of an event and
`A^c` denote the complement of event A.

We know that:

`P(A^c)=1-P(A)`

Now,

`P(A)=(4)/(6)\\\\P(A)=(2)/(3)`

Hence,

`P(A^c)=1-(2)/(3)\\\\P(A^c)=(3-2)/(3)\\\\P(A^c)=(1)/(3)`

Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:

1/3