5
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What is the probability that only $1$ out of the first $4$ you picked are black?

So it is clear that we have picked $4$ balls. Our $4$ spots can be as follows:

$\mathrm{BWWW}$

$\mathrm{WBWW}$

$\mathrm{WWBW}$

$\mathrm{WWWB}$

$4$ ways to orient this.

There are $6$ W balls, from those we must pick $3$.

There are $4$ B balls, from those we must pick $1$.

Thus:

$$\frac{\displaystyle\binom{6}{3}\binom{4}{1}}{\displaystyle\binom{10}{4}}$$

Is this correct?

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  • $\begingroup$ Yes, you interpret "only 1 out of the first 4" as "1 and only 1 out of the first 4". A less likely meaning would be "at most 1 out of the first 4". $\endgroup$ – Jeppe Stig Nielsen Oct 8 '18 at 8:55
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Your answer is correct and is a good example of use of the hypergeometric distribution.

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