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 or 2) = 3/12 b. 12 possible outcomes; p(1 or 2) = 1/3 c. 6 possible outcomes; p(1 or 2) = 1/4 d. 6 possible outcomes; p(1 or 2) = 1/3

Explanation:

Step1: Determine sample - space size

When rolling a standard six - sided die, the sample space \(S=\{1,2,3,4,5,6\}\), so there are \(n(S) = 6\) possible outcomes.

Step2: Determine favorable outcomes

The event \(E\) of getting a 1 or a 2 has \(n(E)=2\) favorable outcomes (\(E = \{1,2\}\)).

Step3: Calculate probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 2\) and \(n(S)=6\) into the formula, we get \(P(1\text{ or }2)=\frac{2}{6}=\frac{1}{3}\).

Answer:

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