Answer to Question #278891 in Statistics and Probability for Sam

Question

A box contains black marbles and white marbles. A person selects two marbles without replacement. If the probability of selecting a black marbles and a white marbles is 15/56, and the probability of selecting a black marble on the first draw is 3/8, find the probability of selecting the white marble on the second draw, given that the first marble selected was a black marble.

(Show tree diagram).

Answer 1

Solution;

Given;

On the first draw;

$P_b=\frac38$

Then ;

$P_w=1-P_b=1-\frac38=\frac58$

Since there is no replacement,there are 7 marbles left in after the first round;

Hence;

The probability if a black is picked in first round are;

$P_{b|b}=\frac27$

$P_{w|b}=\frac57$

While having picked a white are;

$P_{w|w}=\frac47$

$P_{b|w}=\frac37$

From the tree diagram,the probability is $\frac57$