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There are 6 black marbles and 7 white marbles in the bag. Without replacing the marbles, we repeatedly pick a marbles until it is a white one. Call X: the number of marbles until we can pick a white marble.

What is the probability distribution of X? And find E(X), V(X)?

Math. H
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1 Answers1

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At each iteration, we do not have a white marbles only if we have a black one so $$ P(X=0)=7/13 $$ and then for $6\geq k\geq 1$, we have $$ P(X=k)= 6/13 \times 5/12 \times ... \times (6-k+1)/(13-k+1) $$ and $$ P(X\geq 7)=0 $$

user501456
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  • I don't think "X=0" has any meaning in this case. If P(X=0)=7/13, P(X=1)=6/13,..., then P(X=0) + P(X=1) + P(X=2)+... >1 which doesn't make sense – Math. H Nov 12 '17 at 13:19