Question

an urn contains 4 green balls and 9 red balls. if tim chooses 9 balls at random from the urn, what is the probability that he will select 2 green balls and 7 red balls? round your answer to 3 decimal places.

(if necessary, consult a list of formulas.)

Explanation:

Identify the parameters of the problem

Using the Hypergeometric Probability knowledge point

$$
LATEXBLOCK0
$$

Calculate the number of successful outcomes

Using the Combinations knowledge point

$$
LATEXBLOCK1
$$

Calculate the total number of possible outcomes

Using the Combinations knowledge point

$$ \binom{13}{9} = \binom{13}{4} = \frac{13 \times 12 \times 11 \times 10}{4 \times 3 \times 2 \times 1} = 715 $$

Calculate the probability

Using the Hypergeometric Probability knowledge point

$$ P = \frac{216}{715} \approx 0.3020979 $$

Round to three decimal places

$$ P \approx 0.302 $$

Answer:

An urn contains 4 green balls and 9 red balls. If Tim chooses 9 balls at random from the urn, what is the probability that he will select 2 green balls and 7 red balls? Round your answer to 3 decimal places.

<blank>0.302</blank>