Question

question 7
1 pts
the sample space for rolling a six - sided die is ( s={1,2,3,4,5,6} ). to answer the following questions, enter your answer in each box in the form of a simplified fraction such as 1/2, 2/3, and so on.
a) what is the probability of obtaining 4?
b) what is the probability of an outcome larger than 3?
c) what is the probability of an outcome that is no more than 3?

Explanation:

Step1: Recall the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in event \(A\) and \(n(S)\) is the number of elements in the sample space. Here, \(n(S) = 6\) (since \(S=\{1,2,3,4,5,6\}\)).

Step2: Solve part (b)

For an outcome larger than \(3\), the event \(A=\{4,5,6\}\). So \(n(A) = 3\). Then \(P(A)=\frac{n(A)}{n(S)}=\frac{3}{6}=\frac{1}{2}\).

Step3: Solve part (c)

For an outcome that is no more than \(3\), the event \(A=\{1,2,3\}\). So \(n(A)=3\). Then \(P(A)=\frac{n(A)}{n(S)}=\frac{3}{6}=\frac{1}{2}\).

Answer:

b) \(\frac{1}{2}\)
c) \(\frac{1}{2}\)