Question

you roll a 6 - sided die two times. what is the probability of rolling an odd number and then rolling a number less than 3? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate probability of rolling odd number

The odd numbers on a 6 - sided die are 1, 3, 5. So there are 3 favorable outcomes out of 6. The probability $P_1$ of rolling an odd number is $P_1=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability of rolling number less than 3

The numbers less than 3 on a 6 - sided die are 1, 2. So there are 2 favorable outcomes out of 6. The probability $P_2$ of rolling a number less than 3 is $P_2 = \frac{2}{6}=\frac{1}{3}$.

Step3: Calculate combined probability

Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$