A third-grade class has 16 girls and 15 boys. A fourth-grade class has 18 boys and 15 girls. When picking teams for PE, captains will make one selection from the fourth-grade class and one selection from the third-grade class before the other team picks. Assuming everyone has an equally likely chance of being selected, what is the probability that the first captain will choose two boys on the first pick?
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The first captain will always get the class first before anyone else has been picked.
Fourth grade has 18 boys out of 33 total
--> probability = 18/33
= 6/11 (reduced)
Third grade has 15 boys out of 31 total
--> probability = 15/31
Combined probability of picking a boy from each class:
= 6/11 * 15/31
Multiply numerators, and denominators: