Question 530501
The probability of picking a girl on the first pick is:  49/100.
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The probability of picking a girl on the second pick depends on whether a girl was picked first.
If a girl was picked initially, then the probability of picking a girl on the second pick is :  48/99.
If a boy was picked initially, then the probability of picking a girl on the second pick is:  49/99.
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The probability of picking a girl first and second is: 49/100 * 48/99.
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And so forth.
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You need to determine the conditional probabilities to find the chance of picking at least 1 girl.
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<table border="1">

<tr>
<th>1st Pick&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<th>2nd Pick&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<th>3rd Pick&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<th>Probability&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<th>Description&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</tr>

<tr>
<td>P(girl)=49/100&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<td>P(girl)=48/99&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<td>P(girl)=47/98&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<td>P=0.113939394
<td>(A) 3 girls
</tr>

<tr>
<td>"
<td>" 
<td>P(boy)=51/98
<td>P=0.123636364
<td>(B) 2 girls, 1 boy
</tr>

<tr>
<td>"
<td>P(boy)=51/99
<td>P(girl)=48/98
<td>P=0.123636364
<td>(C) 2 girls, 1 boy
</tr>
<tr>
<td>"
<td>"
<td>P(boy)=50/98
<td>P=0.128787879
<td>(D) 1 girl, 2 boys
</tr>

<tr>
<td>P(boy)=51/100
<td>P(girl)=49/99
<td>P(girl)=48/98
<td>P=0.123636364
<td>(E) 2 girls, 1 boy
</tr>

<tr>
<td>"
<td>"
<td>P(boy)=50/98
<td>P=0.128787879
<td>(F) 1 girl, 2 boys</tr>

<tr>
<td>"
<td>P(boy)=50/99
<td>P(girl)=49/98
<td>P=0.128787879
<td>(G) 1 girl, 2 boys
</tr>

<tr>
<td>"
<td>"
<td>P(boy)=49/98
<td>P=0.128787879
<td>(H) 3 boys
</tr>

</table>

The total probability = 1.00, as you can see.
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P(at least 1 girl) = A+B+C+D+E+F+G = 0.871212121
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<b>OR</b>
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You could see the problem in terms of the chance of picking 3 boys.  If you do <b>not</b> pick 3 boys, then you have to pick at least 1 girl.
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P(picking 3 boys) = 51/100 * 50/99 * 49/98 = 0.128787879
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P(picking at least 1 girl) = 1.0 - 0.128787879 = 0.871212121
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Same answer. Two ways to get there.
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Done.