A bag contains 3 red, 5 yellow, 2 green and 6 blue marbles. If one marble is chosen at random, replaced, and then a second marble is chosen at random, find the probability of obtaining 2 marbles of different colors.
prob of two reds = 3/16*3/16 = 9/256
prob of two yell = 5/16*5/16 = 25/256
prob of two green= 2/16*2/16 = 4/256
prob of two blue = 6/16*6/16 = 36/256
so chance we WILL get two of something
= 74/256
so chance we WILL NOT get two the same
= 1- 74/256 = 182/256 = 0.711
To find the probability of obtaining 2 marbles of different colors, we need to determine the total number of possible outcomes (sample space) and the number of favorable outcomes.
Step 1: Find the total number of possible outcomes:
The first marble can be any of the 16 marbles in the bag, and the second marble can also be any of the 16 marbles. Since we are replacing the first marble, the number of possible outcomes for each choice remains the same. Therefore, the total number of possible outcomes is:
16 (choices for the first marble) * 16 (choices for the second marble) = 256.
Step 2: Find the number of favorable outcomes:
To have 2 marbles of different colors, we need to choose one marble that is not red, and one that is not the same color as the first marble chosen.
First, let's find the number of choices for the first marble:
- There are 3 red marbles, so there are 16 - 3 = 13 choices for the first marble.
Now, let's find the number of choices for the second marble:
- We have already chosen one marble that is not red, so the number of choices for the second marble is 16-1 = 15.
Therefore, the number of favorable outcomes is:
13 (choices for the first marble) * 15 (choices for the second marble) = 195.
Step 3: Calculate the probability of obtaining 2 marbles of different colors:
The probability is the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes.
Probability = 195 / 256 ≈ 0.76.
So, the probability of obtaining 2 marbles of different colors is approximately 0.76, or 76%.