Kimberlee Ann

2022-07-23

Suppose a jar contains 13 red marbles and 31 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Round your answer to 4 decimal places.

Andre BalkonE

To find the probability that both marbles drawn from the jar are red, we need to determine the favorable outcomes (drawing 2 red marbles) and the total possible outcomes (drawing any 2 marbles).
Given that the jar contains 13 red marbles and 31 blue marbles, the total number of marbles in the jar is 13 + 31 = 44.
To calculate the probability, we'll consider the concept of combinations. The number of ways to choose 2 red marbles from the 13 available red marbles is given by the combination formula:
$\left(\genfrac{}{}{0}{}{n}{k}\right)=\frac{n!}{k!\left(n-k\right)!}$
where n is the total number of items and k is the number of items chosen.
In this case, we want to calculate the number of ways to choose 2 red marbles from the 13 available red marbles:
$\left(\genfrac{}{}{0}{}{13}{2}\right)=\frac{13!}{2!\left(13-2\right)!}=\frac{13!}{2!11!}=\frac{13×12}{2}=78$
Next, we need to calculate the total number of ways to choose any 2 marbles from the 44 marbles in the jar:
$\left(\genfrac{}{}{0}{}{44}{2}\right)=\frac{44!}{2!\left(44-2\right)!}=\frac{44!}{2!42!}=\frac{44×43}{2}=946$
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Rounded to 4 decimal places, the probability that both marbles drawn are red is approximately 0.0824.

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