Question 1189464
<font color=black size=3>
R = probability of getting red
B = probability of getting blue
G = probability of getting green
These values are between 0 and 1.


We have this given statement
"the probability that a red pen will be chosen is two times the probability for a blue pen and three times the probability for a green pen"


Based on that given info, we can say
R = 2B
R = 3G
We're dealing with the same R value for each equation, so we can equate the two right hand sides
2B = 3G
B = 3G/2
B = 1.5G


Furthermore,
R + B + G = 1
3G + 1.5G + G = 1
5.5G = 1
G = 1/(5.5)
G = 10/55
G = 2/11 is the probability of getting a green pen


B = (3/2)*G
B = (3/2)*(2/11)
B = 3/11 is the probability of getting blue


R = 2B = 2*(3/11) = 6/11
or
R = 3G = 3*(2/11) = 6/11
represents the probability of getting red


If we had 6 red pens out of 11 total, then it would lead directly to 6/11.


Double the values "6 and 11" to get "12 and 22" respectively. This indicates having 12 red pens out of 22 total gives the probability 12/22 = 6/11.
Therefore, it shows that there are 22 pens total in this box.


<font color=red>Answer: 22 pens</font>
</font>