Question

Consider two boxes, one containing one black and one white marble, the other, two black and one white marble. A box is selected at random and a marble is drawn at random from the selected box. What is the probability that the marble is black?

Answer 1

Answer:

$\frac{7}{12}$

Step-by-step explanation:

Probability refers to chance of happening of some event.

Conditional probability is the probability of an event A, given that another event B has already occurred.

$B_1,B_2$ denote the two boxes.

In box $B_1$:

No. of black balls = 1

No. of white balls = 1

In box $B_2$:

No. of black balls = 2

No. of white balls = 1

Let B, W denote black and white marble.

So, probability that either of the boxes $B_1,B_2$ is chosen is $\frac{1}{2}$

Probability that a black ball is chosen from box $B_1$ = $\frac{1}{2}$

Probability that a black ball is chosen from box $B_2=\frac{2}{3}$

To find:probability that the marble is black

Solution:

Probability that the marble is black = $\frac{1}{2}(\frac{1}{2} )+\frac{1}{2}(\frac{2}{3})=\frac{1}{4}+\frac{1}{3}=\frac{7}{12}$