Question

calculate the probability of drawing a blue, followed by a red marble. no replacement. what is the probability of drawing a blue marble?
$\frac{?}{10}\times\frac{2}{}=\frac{}{}=\frac{}{}$

Explanation:

Step1: Count blue marbles

There is 1 blue marble out of 10 marbles initially. So the probability of drawing a blue marble first is $\frac{1}{10}$.

Step2: Calculate probability of red after blue

After drawing a blue marble (no - replacement), there are 9 marbles left. There are 2 red marbles, so the probability of drawing a red marble next is $\frac{2}{9}$.

Step3: Calculate combined probability

The probability of drawing a blue followed by a red is the product of the two probabilities, $\frac{1}{10}\times\frac{2}{9}=\frac{2}{90}=\frac{1}{45}$.

Answer:

$\frac{1}{45}$