Question

You have a brown paper bag that contains 10 burnt orange balls and 10 navy blue balls (these are UVA’s colors where I went to graduate school, undergraduate was at UGA, thus I am a dawg). The balls are drawn at random, one at a time without replacement. Find the probability that the fourth burnt orange ball is the seventh ball drawn. Give your answer to four decimal places.

Answer 1

Total 20 balls

We need 4th brunt in 7th drawn

So, 3 brunt orange got selected in first 6 and 3 navy blue got selected in first 6.

$P=\frac{\binom{10}{3}*\binom{10}{3}}{\binom{20}{6}}*\frac{7}{14}=0.1858$

Hence, 0.1858 is the answer.

Please comment if any doubt. Thank you.