SOLUTION: Please help me. Thank you. Batteries are sold in packs of 10. An inspector selects 2 batteries at random from the pack without replacement. If both batteries work, then the pac

Question 1113213: Please help me. Thank you.
Batteries are sold in packs of 10. An inspector selects 2 batteries at random from the pack without replacement. If both batteries work, then the pack is accepted. If neither works, then the pack is rejected. If one works and one fails, then the inspector selects 2 more batteries from the remaining batteries in the pack. The pack is then accepted only if both batteries work. What is the probability that a pack with 3 defective batteries will be accepted?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
probability that 2 work is 7/10*6/9=42/90 or 14/30.
probability that 1 works and other doesn't is 2*7/10*3/9=42/90 or 14/30
The latter is multiplied by the probability that the next two batteries work, which has a sample space of 8 batteries, 2 of which are defective. This would be 6/8*5/7=30/56 or 15/28
14/30+(14/30)*(15/28)=14/30+ 210/840=0.717

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