Question

4. An urn contains four blue balls and six green balls of the same size so that they are undistinguishable bytouch. Two balls are selected without replacement. Find the following probabilities.(a) The second ball is blue given that the first is green(b) The second ball is blue given that the first ball is blue(c) A blue and a green ball are selected(d) Two blue balls are selected

Answer 1

Step-by-step explanation:

From the information given,

number of blue balls = 4

number of green balls = 6

Total number of balls = 4 + 6 = 10

Probability = number of favorable outcomes/number of total outcomes

Probability of selecting a blue ball = 4/10 = 2/5

Probability of selecting a green ball = 6/10 = 3/5

Since there is no replacement,

Probability of selecting a green ball and blue ball = 6/10 x 4/9 = 4/15

a) This is a conditional probability

The probability that the second ball is blue given that the first is green = (4/15)/(3/5) = 4/15 x 5/3 = 4/9

The probability that the second ball is blue given that the first is green = 4/9

b) This is a conditional probability

The probability of selecting a blue ball and another blue ball = 4/10 x 3/9 = 2/15

The probability that the second ball is blue given that the first is blue = (2/15)/(2/5) = 2/15 x 5/2

The probability that the second ball is blue given that the first is blue = 1/3

c) Probability of selecting a blue and a green ball = 4/10 x 6/9

Probability of selecting a blue and a green ball = 4/15

d) Probability of selecting two blue balls = 4/10 x 3/9

Probability of selecting two blue balls = 2/15