Four defective flashlight batteries are mistakenly mixed withtwo non -defective

Question

Four defective flashlight batteries are mistakenly mixed withtwo non -defective flashlight batteries which all lookidentical. If you randomly choose two betteries withoutreplacement, what is the probabilty that: 1) Both are defective? 2) Both are non-defective? 3) At most, one is non defective? There are 30 possible outcomes Four defective flashlight batteries are mistakenly mixed withtwo non -defective flashlight batteries which all lookidentical. If you randomly choose two betteries withoutreplacement, what is the probabilty that: 1) Both are defective? 2) Both are non-defective? 3) At most, one is non defective? There are 30 possible outcomes

Explanation / Answer

Without Replacement: Hypergeometric distribution 4 defective ones 2 non-defective oens a) P(both are defective)= 4/6 * 3/5 = 12/30 = 2/5 b) P( both are non-defective)= 2/6 * 1/5 = 2/30 =1/15 c) P(at most one is non-defective)= P(0 non-defective or 1non-defective)=1-P(both defective) = 1-2/5=3/5 Good Luck!

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