Two boxes arc labeled I and II Box I contains 4 black balls

Two boxes arc labeled I and II. Box I contains 4 black balls and 6 white balls. Box II contains 2 black balls and 8 white balls. A player randomly selects one box and then randomly draws 2 balls without replacement from the selected box. What is the probability of obtaining 2 black ball Given that 2 black balls arc obtained, what is the probability that Box I is selected Suppose that 20 players conduct the game independently. What is the probability that exactly 4 players obtain 2 black balls

Solution

A) PROBABILITY IF 2 BALLS DRAWN FROM 1ST CASE

= 1/2*4/10*3/9 = 1/15

PROBABILITY IF 2 BALLS DRAWN FROM 2ND CASE

= 1/2*2/10*1/9 = 1/90

IN BOTH THE CASES THE PROBABILITY OF SELECTING THE BOX = 1/2 OF EQUAL CHANCES WHILE IF 1ST BALL IS SELECTED THEN THE TOTAL NUMBER OF BALLS WILL REDUCE AS THIS IS A NON REPLACEMENT QUESTION

B) PROBABILITY OF SELECTING BALL FROM 1 BOX = 1/15

PROBABILITY THAT 1ST BOX SELECTED = 1/2

THEREFORE PROBABILITY THAT 2 BALL SELECTED FROM 1 BOX = 1/2*1/15 = 1/30

C)20 PLAYER ARE THERE

IN TOTAL 20 BALLS

PROBABILITY OF BALCK BALLS = 6/20 = 3/10

PROBABILITY OF WHITE = 14/20 = 7/10

SO N = 20

R = 4

20C4(3/10)^4*(7/10)^16 = 0.130