document.write( "Question 1194851: A box contains 24 bulbs, 3 of which are defective. If two bulbs are selected and tested, find the probability that both are defective. \n" ); document.write( "

Algebra.Com's Answer #827169 by greenestamps(13198) $\"\"$ $\"About$

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\n" ); document.write( "The solution from @Boreal uses one of two primary methods for solving problems like this -- by imagining selecting one bulb at a time and finding the probability that each is defective, then multiplying those probabilities.

\n" ); document.write( "In this problem, that is the much easier method. However, you should know the other primary method, which will be required when the problem is more complex.

\n" ); document.write( "The probability that both bulbs selected are defective is the number of ways 2 of the 3 defective bulbs could be selected, divided by the total number of ways 2 of the 24 bulbs could be selected.

\n" ); document.write( "# of ways to select 2 of the 3 defective bulbs: 3 choose 2 = C(3,2) = 3
\n" ); document.write( "# of ways to select 2 of the 24 bulbs: 24 choose 2 = C(24,2) = (24*23)/2 = 23*12=276

\n" ); document.write( "P(selecting two defective bulbs) = 3/276 = 1/92

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