A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads.

Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.

∴ P(E) =	n(E)	=	7	.
	n(S)		8

Total number of balls = (8 + 7 + 6) = 21.

Let E	= event that the ball drawn is neither red nor green
	= event that the ball drawn is blue.

∴ n(E) = 7.

∴ P(E) =	n(E)	=	7	=	1	.
	n(S)		21		3

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) =	8	=	4	.
	14		7

Let S be the sample space.

Then, n(S) = 52C2 =	(52 x 51)	= 1326.
	(2 x 1)

Let E = event of getting 2 kings out of 4.

∴ n(E) = 4C2 =	(4 x 3)	= 6.
	(2 x 1)

∴ P(E) =	n(E)	=	6	=	1	.
	n(S)		1326		221

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S)	= Number ways of selecting 3 students out of 25
	= 25C3 `
	= (25 x 24 x 23) (3 x 2 x 1)
	= 2300.

n(E)	= (10C1 x 15C2)
	= [ 10 x (15 x 14) ] (2 x 1)
	= 1050.

∴ P(E) =	n(E)	=	1050	=	21	.
	n(S)		2300		46

P (getting a prize) =	10	=	10	=	2	.
	(10 + 25)		35		7

Let T.D. be Re. 1.

Then, B.D. = Rs.	11	= Rs. 1.10.
	10

∴ Sum = Rs.	❨	1.10 x 1	❩	= Rs.	❨	110	❩	= Rs. 11.
		1.10 - 1				10

∴ S.I. on Rs. 11 for 2 years is Rs. 1.10

∴ Rate =	❨	100 x 1.10	❩%	= 5%.
		11 x 2

S.I. on Rs. 1600 = T.D. on Rs. 1680.

∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.

∴ Time =	❨	100 x 80	❩year	=	1	year = 4 months.
		1600 x 15			3

T.D.	= B.D. x 100 100 + (R x T)
	= Rs. [ 420 x 100 ] 100 + ❨ 15 x 1 ❩ 3
	= Rs. ❨ 420 x 100 ❩ 105
	= Rs. 400.

T.D. = √P.W. x B.G. = √576 x 16 = 96.