An urn contains 5 blue and 8 red balls. We choose 6 balls at random. What is the probability that 4 of the 6 balls will be blue? SHOW WORK

P(4 blue balls) = (5C4 * 8C2) / (13C6)

= (5*28) / 1716
= 140/1716
= 0.0814

Did you know?

Did you know that probability is a mathematical concept used to measure the likelihood of an event happening? In the case of an urn containing 5 blue and 8 red balls, if we randomly choose 6 balls, we can calculate the probability of getting 4 blue balls. To find this probability, we can use the formula for combinations, which is expressed as nCr. In this case, we need to calculate the combination of choosing 4 blue balls out of 5 (nCr), multiplied by the combination of choosing 2 red balls out of 8 (nCr), divided by the total combination of choosing any 6 balls out of the total 13 (nCr). Using the combinations formula, we can calculate the probability as follows: P(4 blue balls) = (5C4 * 8C2) / 13C6 Simplifying the equation, we can calculate the individual combinations: 5C4 = 5 (since choosing 4 balls out of 5 only has one option) 8C2 = (8! / (2! * (8-2)!)) = 28 (since choosing 2 balls out of 8 has 28 different combinations) 13C6 = (13! / (6! * (13-6)!)) = 1716 (since choosing 6 balls out of 13 has 1716 different combinations) Plugging the values back into the equation: P(4 blue balls) = (5 * 28) / 1716 Calculating the final value, we find that the probability of choosing 4 blue balls out of 6 randomly selected from the urn is approximately 0.081. Therefore, the probability of getting 4 blue balls out of the 6 chosen from the urn is about 0.081, or 8.1%.