consider the following experiment: rolling a die. what is the sample - space of the experiment? what is the…

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

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

Answer

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})