There are 2 equal boxes with balls First box consists of 3 w

Solution

Dear Friend,

To solve this problem let us apply stepwise approach.

Step 1

First we shall select one box out of the two given boxes.

Let the two boxes be denoted by A and B

Since the boxes are identical,thus probabality of selecting either of the box is same,ie

as there are two boxes(possible outcomes) we can select one box in random.

Thus P(A)=P(B)=1/2

STEP 2

LET C:BE AN EVENT THAT THE BALL SELECTED IS A BLACK BALL.

THUS WE CAN GET A BLACK BALL IF WE SELECT A BLACK BALL FROM BOX A OR FROM BOX 2 i.e

P(SELECTING A BLACK BALL)=P(C/A)+P(B/A)

{NOTE;P(C/A=PROBABILITY OF C SUCH THAT BOX A IS SELECTED

P(C/B)=PROBABILITY OF C SUCH THAT BOX B IS SELECTED}

TO SOLVE FUTHER WE CONSTRUCT A SIMPLE TABLE TO CARRY OUT THE REQUIRED APPROACH

BOX A

Number of black balls

Number of white balls

Total number of balls

1

3

1 + 3 =4

BOX B

Number of black balls

Number of white balls

Total number of balls

4

2

4 +2 = 6

STEP 3

P(SELECTING A BLACK BALL)=

P(SELECTING A BLACK BALL FROM 1ST BOX)

OR

P(SELECTING A BLACK BALL FROM 2ND BOX)

1/8+1/3=(3+8)/24=11/24

ANSWER PROBABILITY OF SELECTING A BLACK BALL FROM EITHER OF THE TWO BOXES IS 11/24