Question

calculate the probability of drawing an orange, followed by another orange marble. no replacement. what is the probability of drawing an orange marble?
\\(\frac{?}{10}\times\frac{2}{ }=\frac{ }{ }=\frac{ }{ }\\)

Explanation:

Step1: Determine initial number of orange marbles

There are 3 orange marbles out of 10 marbles initially. So the probability of drawing an orange marble on the first - draw is $\frac{3}{10}$.

Step2: Determine number of orange marbles and total marbles after first draw

After drawing one orange marble (no replacement), there are 2 orange marbles left and 9 marbles in total. So the probability of drawing an orange marble on the second draw is $\frac{2}{9}$.

Step3: Calculate the combined probability

The probability of both events happening is the product of the probabilities of each event. So we multiply $\frac{3}{10}\times\frac{2}{9}=\frac{6}{90}=\frac{1}{15}$.

Answer:

$\frac{3}{10}\times\frac{2}{9}=\frac{6}{90}=\frac{1}{15}$