Question

consider the following experiment:
rolling a die.
what is the sample space of the experiment? what is the probability of getting a 1 or a 2?
a. 12 possible outcomes; ( p(1 \text{ or } 2)=\frac{3}{12} )
b. 12 possible outcomes; ( p(1 \text{ or } 2)=\frac{1}{3} )
c. 6 possible outcomes; ( p(1 \text{ or } 2)=\frac{1}{4} )
d. 6 possible outcomes; ( p(1 \text{ or } 2)=\frac{1}{3} )

Explanation:

Step1: Determine the sample space

When rolling a die, the possible outcomes are \(1, 2, 3, 4, 5, 6\). So the sample space \(S=\{1,2,3,4,5,6\}\), and the number of elements in the sample space \(n(S) = 6\).

Step2: Calculate the probability of getting a 1 or a 2

Let \(A\) be the event of getting a 1 or a 2. Then \(A=\{1,2\}\), and \(n(A)=2\).
The probability formula is \(P(A)=\frac{n(A)}{n(S)}\).
Substitute \(n(A) = 2\) and \(n(S)=6\) into the formula: \(P(A)=\frac{2}{6}=\frac{1}{3}\).

Answer:

D. 6 possible outcomes; \(P(1\ or\ 2)=\frac{1}{3}\)