Respuesta :
Answer:
= 18 red marbles
Step-by-step explanation:
Let x be the number of red marbles that must be added
Therefore;
New number or red marbles = x+12
Total marbles will be x+32
Thus;
The probability of selecting a red marble = (x+12)/(x+32)
Therefore;
(x+12)/(x+32)=3/5
5(x+12)=3(x+32)
5x+60+3x+96
2x=36
x=18
The number of additional red marbles needed to get the red marble drawing probability as 3/5 is given by: Option B: 18
How to calculate the probability of an event?
Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For the considered case, we're given:
- Number of red marbles in the bag considered =
- Number of yellow marbles =
- Number of green marbles =
We need to add some red marbles in the bag such that the probability of drawing a red marble becomes 3/5 (this 3/5 is not mentioned in question here but is there in real question).
We can take that number of additional red marbles to be denoted by [tex]x[/tex]
Then, total number of red marbles = [tex]x + 12[/tex]
Total number of marbles in the bag = [tex]x + 12 + 5 + 15 = x + 32[/tex]
Total number of ways of selecting one marble from the bag = [tex]^{x+32}C_1 = x + 32[/tex]
Total number of ways of selecting one red marble from the bag = [tex]^{x+12}C_1 = x+12[/tex]
Thus, if event E = selecting a red marble from the considered bag(now modified by adding x red marbles), we get
[tex]P(E) = \dfrac{x+12}{x+32} = \dfrac{3}{5} \: \: \rm (needed)[/tex]
Thus, we get:
[tex]\dfrac{x+12}{x+32} = \dfrac{3}{5}\\\\5x + 60 = 3x + 96\\2x = 36\\x = 18[/tex]
Thus, in the given bag, if we add 18 red marbles, then the probability of drawing a red marble will become 3/5
Thus, The number of additional red marbles needed to get the red marble drawing probability as 3/5 is given by: Option B: 18
Learn more about probability here:
brainly.com/question/1210781
