In a group of 10 batteries, 5 are dead. You choose 2 batteries at random. a) Create a probability model for the number of good batteries you get. b) What's the expected number of good ones you get? c) What's the standard deviation?

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Mathematics

Kadence Cross

9 January, 02:32

In a group of 10 batteries, 5 are dead. You choose 2 batteries at random. a) Create a probability model for the number of good batteries you get. b) What's the expected number of good ones you get? c) What's the standard deviation?

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Jean Horton · Answer 1

You have 10 batteries of which 5 are dead. That means 1/2 of the batteries are dead. So if you randomly select a battery, there is a 50% chance of selecting a dead one, or a good one. But since you're choosing 2, that means the first one you select has a 50% chance of being dead or good, (5/10), but then the second one has a 44% chance of being dead or good, (4/9). multiplying these, you get 22% chance of randomly selecting 2 good batteries.