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 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 (a)

For the event of obtaining a \(4\), \(n(A)=1\) (only one \(4\) in the sample space). So \(P(4)=\frac{1}{6}\).

Step3: Solve part (b)

The outcomes larger than \(3\) are \(4\), \(5\), \(6\). So \(n(A) = 3\). Then \(P(\text{outcome}>3)=\frac{3}{6}=\frac{1}{2}\).

Step4: Solve part (c)

The outcomes no more than \(3\) are \(1\), \(2\), \(3\). So \(n(A)=3\). Then \(P(\text{outcome}\leq3)=\frac{3}{6}=\frac{1}{2}\).

Answer:

a) \(\frac{1}{6}\)
b) \(\frac{1}{2}\)
c) \(\frac{1}{2}\)