Melissa has a bag that contains 6 red marbles, 8 yellow marbles, and 18 blue marbles. If she chooses one marble from the bag, what is the probability that the marble is not blue?
A. $\frac{2}{9}$
B. $\frac{7}{9}$
C. $\frac{7}{16}$
D. $\frac{9}{16}$
Answer (2)
Calculate the total number of marbles: 6 + 8 + 18 = 32 .
Calculate the number of marbles that are not blue: 6 + 8 = 14 .
Calculate the probability of choosing a marble that is not blue: 32 14 = 16 7 .
The probability that the marble is not blue is 16 7 .
Explanation
Understand the problem We are given a bag containing 6 red marbles, 8 yellow marbles, and 18 blue marbles. We want to find the probability of picking a marble that is not blue.
Calculate the total number of marbles First, we need to find the total number of marbles in the bag. We add the number of red, yellow, and blue marbles: 6 + 8 + 18 = 32 So, there are a total of 32 marbles in the bag.
Calculate the number of marbles that are not blue Next, we need to find the number of marbles that are not blue. This includes the red and yellow marbles. So we add the number of red and yellow marbles: 6 + 8 = 14 There are 14 marbles that are not blue.
Calculate the probability Now, we can calculate the probability of picking a marble that is not blue. The probability is the number of 'not blue' marbles divided by the total number of marbles: P ( " N o tBl u e " ) = Total number of marbles Number of not blue marbles = 32 14 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 32 14 = 32 ÷ 2 14 ÷ 2 = 16 7 So, the probability of picking a marble that is not blue is 16 7 .
State the final answer Therefore, the probability that the marble Melissa chooses is not blue is 16 7 .
Examples
Imagine you have a mixed bag of candies with different flavors, and you want to know the chance of picking a candy that isn't cherry-flavored. This is similar to Melissa's marble problem. Knowing the number of each type of candy and the total number of candies, you can calculate the probability of picking a non-cherry candy. This kind of probability calculation is useful in many everyday situations, such as estimating your chances in games or understanding the likelihood of certain events occurring.
The probability that Melissa chooses a marble that is not blue is 16 7 . This is calculated by finding the total number of non-blue marbles and dividing by the total number of marbles. Thus, the correct choice is C . 16 7 .
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