Question

jarod has a bag of 20 marbles containing 12 red, 6 green, and 2 blue marbles. jarod selects two marbles at random without replacement. what is the probability that jarod selects two red marbles? a $\frac{1}{190}$ b $\frac{1}{10}$ c $\frac{33}{95}$ d $\frac{9}{28}$

Explanation:

Step1: Calculate probability of first red - marble

The probability of selecting a red marble on the first draw is the number of red marbles divided by the total number of marbles. There are 12 red marbles and 20 total marbles, so the probability $P_1=\frac{12}{20}$.

Step2: Calculate probability of second red - marble

Since we are drawing without replacement, after the first red - marble is drawn, there are 11 red marbles left and 19 total marbles left. So the probability of drawing a second red marble is $P_2 = \frac{11}{19}$.

Step3: Calculate the probability of both events

The probability of both events (drawing two red marbles) occurring is the product of the probabilities of each event. So $P = P_1\times P_2=\frac{12}{20}\times\frac{11}{19}=\frac{12\times11}{20\times19}=\frac{132}{380}=\frac{33}{95}$.

Answer:

C. $\frac{33}{95}$