Jeff has 8 red marbles, 6 blue marbles, and 4 green marbles that are the same size and shape. He puts the marbles into a bag, mixes them, and randomly picks one marble. What is the probability that the marble will be blue
The Correct Answer and Explanation is:
To find the probability that Jeff randomly picks a blue marble from the bag, we follow these steps:
Step 1: Determine the total number of marbles.
- Red marbles = 8
- Blue marbles = 6
- Green marbles = 4
Total marbles = 8 + 6 + 4 = 18
Step 2: Find the number of favorable outcomes.
We are interested in the probability that the marble picked is blue. There are 6 blue marbles.
Step 3: Use the probability formula.
Probability=Number of favorable outcomesTotal number of possible outcomes=618=13\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{6}{18} = \frac{1}{3}
✅ Final Answer:
13\boxed{\frac{1}{3}}
Explanation:
Probability is a measure of how likely an event is to occur. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, assuming all outcomes are equally likely.
In this case, Jeff has three colors of marbles: red, blue, and green. There are 8 red marbles, 6 blue marbles, and 4 green marbles. All marbles are the same in size and shape, so there is no bias or preference in picking any particular color—they all have an equal chance of being picked.
To find the total number of marbles in the bag, we simply add the quantities of each color together:
8 (red) + 6 (blue) + 4 (green) = 18 total marbles.
The event we are interested in is picking a blue marble. There are 6 blue marbles in the bag, so there are 6 favorable outcomes.
Now, we apply the basic probability formula: Probability of blue marble=Number of blue marblesTotal number of marbles=618\text{Probability of blue marble} = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{6}{18}
We can simplify this fraction by dividing the numerator and the denominator by 6, which gives: 6÷618÷6=13\frac{6 \div 6}{18 \div 6} = \frac{1}{3}
This means that if Jeff picks one marble at random, there is a 1 in 3 chance, or approximately 33.33%, that it will be blue.
