AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
Expert: Paul Klarreich Date: 5/14/2008 Subject: probability
Question In a pile of 40 oranges, 10 are rotten. What is the probability of getting at least 3 rotten oranges if 20 oranges are picked at random? Please explain..
Answer Questioner: jagdeep
Category: Advanced Math
Private: No
Subject: probability
Question: In a pile of 40 oranges, 10 are rotten. What is the probability of getting at least 3 rotten oranges if 20 oranges are picked at random? Please explain..
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Hi, jagdeep,
If you pick 20 out of 40, there are C(40,20) possible subsets.
0. What is p(0)? i.e p(zero rottens)
Of these, C(30,20) will contain no rotten ones. So
p(0) = C(30,20)/C(40,20)
1. What is p(1)? You want a subset with 1 rotten, 19 good.
There are C(10,1) 1-element subsets of rottens.
There are C(30,19) 19-element subsets of goods.
The product is C(10,1)C(30,19), so
p(1) = C(10,1)C(30,19)/C(40,20)
2. What is p(2)? You want a subset with 2 rotten, 18 good.
There are C(10,2) 2-element subsets of rottens.
There are C(30,18) 18-element subsets of goods.
The product is C(10,2)C(30,18), so
