Question

Two balls are drawn at random with replacement from a box containing 15 red and 10 white balls. Calculate the possibility that
(a) both balls are red
(b) first ball is red and second is white
(c) one of them is white and the other is red

Answer 1

a.7/25

b.10/25

c.25/25 =1

Answer 2

Answer:

(a) 9 / 25

(b) 6 / 25

(c) 12 / 25

Step-by-step explanation:

First, we need:

• P(first red) = P(second red)  [ since this is with replacement ] = (# red) / (# balls) = 15 / 25 = 3/5
• P(first white) = P(second white) = (# white) / (# balls) = 10 / 25 = 2/5

(a)  P(both red)

= P(first red) × P(second red)

= 3/5 × 3/5

= 9 / 25

(b) P(first red and second white)

= P(first red) × P(second white)

= 3/5 × 2/5

= 6 / 25

(c) P(one white and the other red)

= P( (first red and second white) OR (first white and second red) )

= P(first red and second white)   +   P(first white and second red)

= 6 / 25  +  P(first white) × P(second red)

= 6 / 25  +  2/5 × 3/5

= 6 / 25  +  6 / 25

= 12 / 25