a bag contains 6 blue marbles and 10 red marbles. If you choose one marble at random, and then another marble at random, what is the probability that both marbles are blue?
first blue:
6/16
second blue
5/15
so
3/8 * 1/3 = 1/8 = 0.125
To find the probability that both marbles are blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Calculate the total number of possible outcomes.
Initially, there are 16 marbles in the bag (6 blue and 10 red). When you pick one marble out of the bag, there are now 15 marbles left in the bag. Therefore, the total number of possible outcomes is equal to choosing one marble out of the 16 marbles, then choosing another marble out of the 15 remaining marbles.
Total possible outcomes = 16 * 15 = 240
Step 2: Calculate the number of favorable outcomes.
To choose two blue marbles, the first marble selected must be blue (6 blue marbles) and the second marble must also be blue (5 blue marbles left).
Number of favorable outcomes = 6 * 5 = 30
Step 3: Calculate the probability.
Probability = Number of favorable outcomes / Total possible outcomes
Probability = 30 / 240
Probability = 1 / 8
Therefore, the probability that both marbles are blue is 1/8 or 0.125 (12.5%).
To find the probability that both marbles are blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Determine the total number of marbles
In this problem, there are a total of 6 blue marbles and 10 red marbles, so the total number of marbles is 6 + 10 = 16.
Step 2: Determine the number of favorable outcomes
In order for both marbles to be blue, we need to choose a blue marble for the first draw and another blue marble for the second draw. There are 6 blue marbles to choose from initially and 5 blue marbles remaining after the first draw.
Step 3: Calculate the probability
The probability of selecting a blue marble on the first draw is 6/16 (as there are 6 blue marbles out of 16 total marbles).
After selecting a blue marble on the first draw, the probability of selecting another blue marble on the second draw is 5/15 (as there are 5 blue marbles remaining out of 15 total marbles).
To find the probability of both marbles being blue, we multiply the probabilities of each individual event:
Probability = (6/16) * (5/15) = 30/240 = 1/8 = 0.125
Therefore, the probability that both marbles drawn are blue is 0.125 or 12.5%.