Question

question 12 points 2

if a die is rolled two times, find the probability of getting \2 or 4\ twice.

\\(\frac{2}{3}\\)

\\(\frac{1}{9}\\)

Explanation:

Identify single roll outcomes

Using the Simple Events knowledge point
A standard six-sided die has the sample space:

$$ S = \{1, 2, 3, 4, 5, 6\} $$

The event \(E\) of rolling a "2 or 4" on a single roll corresponds to the subset:

$$ E = \{2, 4\} $$

The probability of this event occurring on a single roll is:

$$ P(E) = \frac{|E|}{|S|} = \frac{2}{6} = \frac{1}{3} $$

Calculate combined probability

Using the Independent Events and Probability with Replacement knowledge points

$$ P(\text{getting "2 or 4" twice}) = P(E) \times P(E) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9} $$

Answer:

• (A) \(\frac{2}{3}\)
• (B) \(\frac{1}{9}\) (Correct answer)