In problems involving drawing balls from a bag or drawing cards, it is important to “count the objects as distinct.”
Example ①
A bag contains 3 red balls and 2 white balls. When one ball is drawn, find the probability of drawing a red ball.
Solution: There are 5 possible outcomes in all and 3 red balls. P = 3/5
A bag contains 3 red balls and 2 white balls. When one ball is drawn, find the probability of drawing a red ball.
Solution: There are 5 possible outcomes in all and 3 red balls. P = 3/5
Example ② (Drawing 2 Balls)
When 2 balls are drawn at the same time from the same bag, find the probability that both are red. (Distinguish the balls as R1,R2,R3,W1,W2.)
Solution: In all = C(5,2) = 10 outcomes. 2 red balls = C(3,2) = 3 outcomes. P = 3/10.
When 2 balls are drawn at the same time from the same bag, find the probability that both are red. (Distinguish the balls as R1,R2,R3,W1,W2.)
Solution: In all = C(5,2) = 10 outcomes. 2 red balls = C(3,2) = 3 outcomes. P = 3/10.
Key Points
- Count balls of the same color as distinct objects (such as R1, R2, R3)
- Check whether order matters
Practice Problems
- There are 5 cards numbered 1〜5. When 2 cards are drawn, find the probability that the sum of their numbers is 6.
Answers and Explanations
- Answer: 2/5. In all, C(5,2)=10 outcomes. A sum of 6 occurs in (1,5)(2,4), or 2 outcomes. 2/10=1/5.