Question

# Exercise 2 A box contains 3 white balls, 4 red balls and 5 black balls. A...

Exercise 2 A box contains 3 white balls, 4 red balls and 5 black balls. A ball is picked, its color recorded and returned to the box(with replacement). Another ball is then selected and its color recorded.

1. Find the probability that 2 black balls are selected.

2. Find the probability that 2 balls of the same color are selected.

Now 4 balls are picked with replacement

3.Find the probability no red balls are selected.

4.Find the probability that the fourth ball selected is the first occurrence of the color white?

Number of white balls = 3

Number of red balls = 4

Number of black balls = 5

Total number of balls = 3 + 4 + 5 = 12

1. P(2 black balls are selected) = (5/12)2

= 0.1736

2. P(2 balls of same color) = (3/12)2 + (4/12)2 + (5/12)2

= 0.3472

3. P(red ball) = 4/12 = 1/3

P(not a red ball) = 1 - 1/3 = 2/3

P(no red balls) = (2/3)4

= 0.1975

P(white) = 3/12 = 0.25

P(not white) = 1 - 0.25 = 0.75

P(fourth ball selected is the first occurrence of the color white) = P(first 3 balls are not white) x P(fourth ball is white)

= 0.753 x 0.25

= 0.1055

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