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
Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:
1/3
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,
\(P(A)=\dfrac{4}{6}\\\\P(A)=\dfrac{2}{3}\)
Hence,
\(P(A^c)=1-\dfrac{2}{3}\\\\P(A^c)=\dfrac{3-2}{3}\\\\P(A^c)=\dfrac{1}{3}\)
Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:
1/3