Question

There are 10 marbles in a bag. Four are blue, 3 are black and 2 white and 1 red. If the marbles are not replaced once they are drawn, find P(black and then white) *

Answer 1

Given:

Given that there are 10 marbles in a bag. 4 are blue, 3 are black, 2 are white and 1 is red.

The marbles are selected by not replacing the drawn ones.

We need to the probability of selected a black marble and then a white marble without replacement.

Probability:

Let B denote the black marble.

Let W denote the white marble.

The probability of selecting a black marble is $P(B)=\frac{3}{10}$

The probability of selecting a white marble without replacement is $P(W)=\frac{2}{9}$

The probability of selecting a black marble and then a white marble without replacement is given by

$P(B \ and \ W)=P(B) \cdot P(W)$

Substituting the values, we get;

$P(B \ and \ W)=\frac{3}{10} \cdot \frac{2}{9}$

$P(B \ and \ W)=\frac{6}{90}$

$P(B \ and \ W)=\frac{1}{15}$

Thus, the probability of selecting a black marble and then a white marble without replacement is $\frac{1}{15}$