A bag contains x marbles. Half of the marbles are blue. Four less than the number of blue marbles are red. The remaining marbles are purple. What is the probability of choosing a purple marble at random?
a. 2
b. 4
c. 1/2-(x/2-4)/x
d. x/2-4
e. x/2
please answer and explain
blue: x/2
red blue-4 = x/2-4
purple: 4
P(purple) = 4/x
crudely put, (c)
To find the probability of choosing a purple marble at random, we need to determine the number of purple marbles in the bag.
Given that half of the marbles are blue, we can conclude that the number of blue marbles is x/2.
It is also mentioned that four less than the number of blue marbles are red. So, the number of red marbles can be calculated as (x/2) - 4.
Since the total number of marbles in the bag is x, we can find the number of purple marbles by subtracting the combined number of blue and red marbles from the total.
The number of purple marbles = x - [(x/2) + ((x/2) - 4)]
= x -(x/2 + x/2 - 4)
= x - (2x/2 - 4)
= x - (x - 4)
= x - x + 4
= 4
So, the number of purple marbles is 4.
Now, the probability of choosing a purple marble at random is calculated by dividing the number of purple marbles by the total number of marbles in the bag, which is x.
Therefore, the probability is 4/x.
In the given answer choices, the correct option is c. 1/2 - (x/2 - 4)/x, as it represents the probability 4/x.
To further simplify the answer, we can rewrite it as c. (2 - x/2) / x.
So, the final answer is c. (2 - x/2) / x.