Mathematics
Mathematics
Problem
An urn contains 5 green, 7 yellow and 8 red balls. Two balls are drawn one after the other. a. (i) If each ball drawn is replaced before the next draw, calculate the probability of obtaining one red and one green ball in any order. b. (ii) If the first ball drawn is not replaced, calculate the probability of obtaining one red and one green ball in any order. c. (iii) Compare the answers obtained in parts (i) and (ii).Intuitive explanation
The key here is recognizing that drawing "one after the other" means the first ball affects what's available for the second draw—this is sampling without replacement. You'll need to think about how probabilities change: after removing the first ball, there are fewer total balls and possibly fewer of a particular color. The trick is deciding whether you care about order (green then yellow is different from yellow then green) or just the combination of colors drawn.
Intuitive explanation
The key here is recognizing that drawing "one after the other" means the first ball affects what's available for the second draw—this is sampling without replacement. You'll need to think about how probabilities change: after removing the first ball, there are fewer total balls and possibly fewer of a particular color. The trick is deciding whether you care about order (green then yellow is different from yellow then green) or just the combination of colors drawn.