Question

you roll a fair six - sided die twice. what is the probability that the die shows an odd number on the first roll and a number less than 5 on the second roll?

Explanation:

Step1: Find probability of odd first roll

There are 3 odd numbers (1,3,5) on a 6-sided die.
$P(\text{odd first roll}) = \frac{3}{6} = \frac{1}{2}$

Step2: Find probability of <5 on second roll

There are 4 numbers less than 5 (1,2,3,4) on a 6-sided die.
$P(\text{<5 second roll}) = \frac{4}{6} = \frac{2}{3}$

Step3: Multiply independent probabilities

Since the two rolls are independent, multiply the two probabilities.
$P(\text{combined}) = \frac{1}{2} \times \frac{2}{3}$

Answer:

$\frac{1}{3}$