# A box contains some black balls and 30 white balls.

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A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.

by (-4,941 points)

Let the number of Black  Balls = x

White Balls = 30

Total balls = x + 30

P(Black Ball) = x/(x + 30)

P(White Ball) = 30/(x + 30)

According  to the question

P(Black Ball ) = 2/5 P(White Ball)

x/(x + 30) = 2/5 × 30/(x + 30)

or      x = 2/5 × 30

x = 12

∴    Number of black Balls = 12

by (-3,444 points)

In randomly drawing a card from 52 cards

n (s) = 52

(i) Let A denote the event that the drawn card is red.

n (A) = 26

∴ P(A) = n (A)/n (S) = 26/52 = ½

(ii) Let B denote the event that drawn card is an ace

n (B) = 4

n (s) = 52

P (B) = ?

∴ P (B) = n (B)/n (S) = 4/52 = 1/13

(iii) Let C denote the event that the drawn card is red and a king.

n ( C ) = 2

P (C ) = ?

n (S) = 52

∴ p (c) = n ( C )/n ( S )

= 2 /52 = 1/26

(IV) Let D denote the event that the drawn card is red or a king

n (D ) = 26 (red cards) + 2 (kings)

= 28

P (D) =?

n(S ) = 52

∴ P (D) = n (D)/n (S) = 28/52 = 7/13