Question

11. a bag contains 8 red marbles, 9 yellow marbles, and
7 green marbles. how many additional red marbles
must be added to the 24 marbles already in the bag so
that the probability of randomly drawing a red marble
is
15.
a 11
b. 16
c. 20
d. 24
e. 32

Answer 1

To get a probability of 3/5, 16 red marbles must be added.

How many additional red marbles must be added?

There are 8 red, 9 yellow, and 7 green marbles, for a total of:

8 + 9 + 7 = 24.

The probability of getting a particular color of marble is given by the quotient between the number of marbles of that color and the total number of marbles.

Here, we want to get a probability of drawing a red marble equal to 3/5.

So, if we add x red marbles, the probability of getting a red marble will be:

P = (8 + x)/(24 + x)

And that must be equal ot 1/5, then we write:

(3/5) = (8 + x)/(24 + x)

If we multiply both sides bt (24 + x), we will get:

3*(24 + x)/5 = 8 + x

Now we can solve that for x.

3*24/5 - 8 = x - x(3/5) = (2/5)*x

x = (3*24/5)*(5/2) - (5/2)*8 = 16

So 16 red marbles must be added, the correct option is b.

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

#SPJ1