a bag contains red blue yellow green and purple marbles all of which are the same size. the probability of selecting a single marble for two of the colors is shown in the table. the probability os selecting e red or a yellow marble is 5/16 the probability of selecting a green marble is twice the probability of selecting a yellow marble what is the probability of selecting a green marble
Let's denote the probability of selecting a red marble as P(R), the probability of selecting a blue marble as P(B), the probability of selecting a yellow marble as P(Y), the probability of selecting a green marble as P(G), and the probability of selecting a purple marble as P(P).
From the information given:
P(R) = 1/8
P(B) = 1/4
P(Y) = x
P(G) = 2x
P(P) = unknown
We also know that the sum of all probabilities must be equal to 1:
P(R) + P(B) + P(Y) + P(G) + P(P) = 1
Substitute the given probabilities and the probabilities in terms of x into the equation:
1/8 + 1/4 + x + 2x + P(P) = 1
1/8 + 1/4 + 3x + P(P) = 1
3/8 + 3x + P(P) = 1
3x + P(P) = 5/8
We also know that the probability of selecting a red or a yellow marble is 5/16:
P(R) + P(Y) = 5/16
1/8 + x = 5/16
x = 5/16 - 1/8
x = 5/16 - 2/16
x = 3/16
Now, substitute the value of x back into the equation for P(G):
P(G) = 2(3/16)
P(G) = 6/16
P(G) = 3/8
Therefore, the probability of selecting a green marble is 3/8.