Question

1. a bag contains 3 red marbles and 2 blue marbles. one marble is drawn without replacement, then a second marble is drawn. what is the probability that both marbles are red? simplified fraction: \square simplified fraction: \square percent: \square %

Explanation:

Step1: Calculate total initial marbles

Total marbles = $3 + 2 = 5$

Step2: Probability first marble red

$P(\text{first red}) = \frac{3}{5}$

Step3: Probability second marble red (no replacement)

Remaining red marbles = 2, total remaining marbles = 4
$P(\text{second red}) = \frac{2}{4} = \frac{1}{2}$

Step4: Multiply probabilities for both red

$P(\text{both red}) = \frac{3}{5} \times \frac{1}{2} = \frac{3}{10}$

Step5: Convert fraction to percent

$\frac{3}{10} \times 100 = 30\%$

Answer:

Simplified Fraction: $\frac{3}{10}$
Percent: $30\%$