Question

suppose a jar contains 13 red marbles and 40 blue marbles. if 2 marbles are randomly chosen from the jar at the same time, find the probability that both marbles are red. round your answer to four decimal places.

Explanation:

Step1: Calculate total number of marbles

The total number of marbles is the sum of red and blue marbles. So, $13 + 40=53$ marbles.

Step2: Calculate probability of first - red marble

The probability of choosing a red marble on the first draw is $\frac{13}{53}$ since there are 13 red marbles out of 53 total marbles.

Step3: Calculate probability of second - red marble

After one red marble is drawn, there are 12 red marbles left and 52 total marbles left. So the probability of choosing a red marble on the second draw given that the first one was red is $\frac{12}{52}$.

Step4: Calculate probability of both red

By the multiplication rule for independent events (in the case of non - replacement, we use the multiplication of conditional probabilities), the probability that both marbles are red is $\frac{13}{53}\times\frac{12}{52}=\frac{13\times12}{53\times52}=\frac{156}{2756}\approx0.0566$.

Answer:

$0.0566$