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suppose we have an "infinite" supply of AA batteries, 75% of which are good (and 25%...

suppose we have an "infinite" supply of AA batteries, 75% of which are good (and 25% of which are bad). if we randomly select two batteries (without replacement) from this supply then find the probability that ...

A) they are both good

B) exactly one of them is good

Math   Statistics-And-Probability   
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Answer #1

Let be the event of a selected AA battery being good and be the event of a selected AA battery being bad.

Given P() = 75/100 = 0.75, P() = 25/100 = 0.25

A) Probability that they are both good = = = 0.75*0.75 = 0.5625 (Since both are independent events)

B) Probability that exactly one of them is good = + = + (Since both are independent events)

= 2*0.75*0.25 = 0.375

Note:

For independent events, =

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