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\n" ); document.write( "In an obscure way, the problem is asking what the probability is that, of the first 5 customers helped, either 2 or 3 or 4 or 5 are women.
\n" ); document.write( "The customers are 6 women and 5 men, so the probability that any one woman is helped is 6/11 and the probability that any one man is helped is 5/11.
\n" ); document.write( "We could find the answer by computing the probabilities of having only 0 or 1 women among the first 5 helped and subtract that from 1.
\n" ); document.write( "Or we could find the answer by computing the probabilities that 2 to 5 women are among the first 5 helped and add those.
\n" ); document.write( "But for learning purposes, I would suggest that it is useful to compute the probabilities for ALL the cases. That is only a bit more work than is required; it gives the student practice in computing such probabilities; and it gives the student a check on his computations by verifying that the sum of the probabilities for all the cases is 1.
\n" ); document.write( "So let's do that. Since we want to verify that the sum of all the probabilities is 1, we will leave each probability in exact fraction form rather than in approximate decimal form.
\n" ); document.write( "P(0 women):
\n" ); document.write( "P(1 woman):
\n" ); document.write( "P(2 women):
\n" ); document.write( "P(3 women):
\n" ); document.write( "P(4 women):
\n" ); document.write( "P(5 women):
\n" ); document.write( "Verify that the sum of the probabilities is 1:
\n" ); document.write( "
\n" ); document.write( "The probabilities for the different cases are correct, so we can find the answer to the problem:
\n" ); document.write( "ANSWER: The probability that among the first 5 customers served at least 2 are women is
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