Two balls are drawn in succession out of a box containing 4 red and 3 white balls. Find the probability that at least 1 ball was red, given that the first ball was (A) Replaced before the second draw. (B) Not replaced before the second draw.

A) 40/49

B) 36/42

Step-by-step explanation:

Given:

Red Balls, R : 4

White Balls, W : 3

Total Balls : 3+4=7 balls

A) If balls were replaced before the 2nd draw

P (White) = 3/7; P (Red) = 4

P (at least 1 red ball),

= 1 - P (no red balls)

= 1 - P (White, White)

= 1 - (3/7) (3/7)

= 1 - (9/49)

= 40/49

A) If balls were replaced before the 2nd draw

P (1st White Ball) = 3/7; P (2nd White Ball) = 2/6

P (at least 1 red ball),

= 1 - P (no red balls)

= 1 - P (1st White, 2nd White)

= 1 - (3/7) (2/6)

= 1 - 6/42

= 36/42