Question

There are 10 marbles in a jar. They are identical except for color. Four are Red, three are Blue, two are Yellow and one is White. You draw a marble from the jar, note its color, and set it aside. Then, you draw another marble from the jar and note its color.

a) What is the probability that you draw two Red marbles?

b) What is the probability that you draw a Blue marble GIVEN that you have drawn a Red one?

c) What is the probability that you draw a Blue and a Yellow marble in EITHER ORDER?

d) What is the probability that EITHER marble you draw is White?

Answer 1

SOLUTION-

NO OF MARBLES=10

RED MARBLES= 4, BLUE MARBLES=3,YELLOW MARBLES=2,WHITE MARBLES=1

MARBLES ARE PICKED AND SET ASIDE (WITHOUT REPLACEMENT).

TWO MARBLES ARE DRAWN.

1.) P(BOTH MARBLES ARE RED) = P( FIRST MARBLE IS RED AND KEPT ASIDE AND THE SECOND ONE IS ALSO RED)

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

2.) LET A BE THE EVENT THAT FRST MARBLE DRAWN IS RED AND B THE EVENT THAT SECOND MARBLE TO BE DRAWN IS BLUE.

P(B|A) = P(A B)/P(A)

NOW, P(A B) = 4/10*3/9 = 2/15

P(A) = 4/10 = 2/5

HENCE, P(B|A) = (2/15)/(2/5) = 1/3

3.) THE PATTERN FOR DRAWING A BLUE AND YELLOW MARBLE IN EITHER ORDER IS,

P(FIRST MARBLE IS YELLOW, SECOND IS BLUE)+P(FIRST MARBLE IS BLUE, SECOND IS YELLOW)

= 2/10*3/9 + 3/10*2/9

= 2/15

4.) EITHER MARBLE IS WHITE MEANS ANY ONE MARBLE IS WHITE AND THE OTHER OF ANY REMAINING COLOUR

= P( FIRST MARBLE IS WHITE, SECOND OF ANY COLOUR) + P(FISRT MARBLE IS OF ANY COLOUR, SECOND IS WHITE)

= (1/10 * 1/9 )+ (1/9* 1/9)

= 19/810

**REMARK**- IN CASE OF DOUBT, COMMENT BELOW AND DO LIKE THE SOLUTION.