Lisa has 9 rings in her jewelry box. Five are gold and 4 are silver. If she randomly selects 3 rings to wear to a party, what is P(2 silver or 2 gold)?

Could you please use specific steps in explaining how to find this probability?
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Let's suppose that Lisa first picks a silver ring. Since there are 4 silver rings, she has a probability of 4/9. That leaves 8 rings, 3 silver and 5 gold. The second ring she picks is also silver, and the probability of picking another is 3/8. So the combined probability of picking 2 silver rings is 4/9*3/8=1/6. The third ring is gold, and there are 5 left in the remaining 7 rings, so the probability is 5/7, and the probability of picking another gold ring from the remaining 6 rings, 2 silver and 4 gold, is 4/6 or 2/3. The combined probability for the selection of rings is 1/6*5/7*2/3=5/63.

But we haven't finished yet because there are other permutations that give us the same selection:

SSGG, SGSG, GSGS, GGSS, GSSG, SGGS all contain two silver (S) and two gold (G). That improves the chances by a factor of six, because 6 permutations produce the same combination, so we multiply by 6: 6*5/63=10/21=0.4762, 47.62%.

by Top Rated User (982k points)

Related questions

1 answer
asked Oct 9, 2021 in Statistics Answers by Noor Level 1 User (120 points) | 99 views
1 answer
1 answer
asked Jul 13, 2013 in Statistics Answers by Leon89 Level 1 User (160 points) | 638 views
1 answer
asked Mar 24, 2013 in Statistics Answers by Akilie Level 1 User (140 points) | 921 views
1 answer
asked Aug 11, 2014 in Statistics Answers by anonymous | 780 views
2 answers
1 answer
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,974 questions
95,835 answers
24,325 users