Question

calculate the probability of drawing a blue, followed by a red marble. no replacement. what is the probability of drawing a red marble? $\frac{1}{10}\times\frac{2}{?}=\frac{2}{}$

Explanation:

Step1: Calculate probability of first - draw

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 second - draw

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 second is $\frac{2}{9}$.

Step3: Calculate combined probability

The probability of drawing a blue followed by a red (no replacement) is the product of the two probabilities. So we multiply $\frac{1}{10}$ by $\frac{2}{9}$, which gives $\frac{1\times2}{10\times9}=\frac{2}{90}=\frac{1}{45}$.

Answer:

$\frac{1}{45}$