Question

Topic: Choosing ping-pong balls without replacement. There are 6 white and 3 orange ping-pong balls in a brown paper bag. Two balls are randomly chosen. Enter your answers as fractions. (The "Preview" simply displays your answer in nice mathematical text. It does not mean that your answer is either right or wrong.) a) How many total balls are in the bag? Preview b) What is the probability that the 1st ball is orange? P(1st = orange) = Preview c) What is the probability that the 2nd ball is also orange, given that the 1st ball was orange? P(2nd = orange | 1st = orange) = Preview d) What is the probability that both the 1st and the 2nd balls are orange?

Answer 1

Answer: a. 9

b. 1/3

c. 1/4

d. 1/12

Step-by-step explanation:

White balls = 6

Orange balls = 3

a. Total number of balls = 6 + 3

= 9

Total balls in bag = 9

b) Probability that the first ball is orange

= No. of orange balls / Total no. of balls

= 3 / 9

= 1 / 3

c) To give the required probability

If one ball being the orange ball has been taken out then the remainder are,

Total balls = 8

If Orange balls = 2

Therefore the probability that the 2nd ball is also orange, given that the 1st ball was orange will be denoted by,

= P(2nd ball|1st orange)

= 2 / 8

= 1 / 4

d) To give the probability that both the 1st and the 2nd balls are orange you multiple their probabilities.

Probability = 1 / 3 * 1 / 4

= 1 / 12