Question

suppose a jar contains 6 red marbles and 10 blue marbles. if you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Explanation:

Step1: Calculate total marbles

The total number of marbles is $6 + 10=16$.

Step2: Calculate probability of first - red marble

The probability of picking a red marble on the first draw is $\frac{6}{16}$.

Step3: Calculate probability of second - red marble

After drawing one red marble, there are 5 red marbles left and 15 marbles in total. So the probability of picking a red marble on the second draw is $\frac{5}{15}$.

Step4: Calculate the probability of both events

Since these are independent - like events (in the sense of non - replacement but sequential probability calculation), the probability that both marbles are red is the product of the probabilities of each event. So $P=\frac{6}{16}\times\frac{5}{15}=\frac{30}{240}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$