Question

1. if an ordinary number cube is rolled twice, what is the probability of rolling an even number and then an odd number?

a. \\(\frac{1}{4}\\)

b. \\(\frac{1}{2}\\)

c. \\(\frac{3}{4}\\)

d. \\(\frac{1}{3}\\)

Explanation:

🆕 New Concept Discovered: Probability of Independent Events
Multiplying individual probabilities for consecutive events.

Step 1: Probability of rolling an even number

An ordinary number cube has 6 sides: \( \{1, 2, 3, 4, 5, 6\} \).

The even numbers are \( \{2, 4, 6\} \) (3 outcomes).

$$ P(\text{Even}) = \frac{3}{6} = \frac{1}{2} $$

Step 2: Probability of rolling an odd number

The odd numbers are \( \{1, 3, 5\} \) (3 outcomes).

$$ P(\text{Odd}) = \frac{3}{6} = \frac{1}{2} $$

Step 3: Combined probability of both events

Since the two rolls are independent, multiply their individual probabilities:

$$ P(\text{Even and then Odd}) = P(\text{Even}) \times P(\text{Odd}) $$

$$ P(\text{Even and then Odd}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $$

Answer:

A. \(\frac{1}{4}\)