2 Balls are selected one at a time with replacement from a b

2. Balls are selected one at a time with replacement from a box containing four red and six white balls. Find the probability that the (a) first ball is red; (b) first two balls are red; (c) third ball is red; (d) third ball is red if the first two balls were red; (e) third ball is red if the first ball was red. 3. Redo Q2 if the balls are selected without replacement.

Solution

Number of red balls = 4

Number of white balls = 6

Total balls = 10

(2) With replacement, number of balls even after withdrawl will remains same i.e 10 .

(a) Required probability - RP = 4/10 = 2/5

(b) RP = 4/10 * 4/10 =4/25

(c) RP = 4/10

(d) RP = 4/10 * 4/10 * 4/10 = 8/125

(e) RP = 4/10 * 4/10 * 4/10 + 4/10 * 6/10 * 4/10 = 4/25

(3) In replacement Case ,  number of balls after withdrawl will decrease by 1.

(a) RP = 4/10

(b) RP = 4/10 * 3/9 = 2/15.

(c) RP = (4/10 * 3/9 * 2/8) + (4/10 * 6/9 * 3/8) +( 6/10 * 5/10 * 4/8) + (6/10 * 4/9 * 3/8) = 23/60.

(d) RP = 4/10 * 3/9 * 2/8 = 1/30

(e) RP = (4/10 * 3/9 * 2/8) + (4/10 * 6/9 * 3/8) = 2/15 .