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)=(3)/(10)`

The probability of selecting a white marble without replacement is
`P(W)=(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)=(3)/(10) \cdot (2)/(9)`

`P(B \ and \ W)=(6)/(90)`

`P(B \ and \ W)=(1)/(15)`

Thus, the probability of selecting a black marble and then a white marble without replacement is
`(1)/(15)`