Problem Solving

I ran into this on the gmatpill prep test

"There are 1,200 golf balls in a golf ball dispensing machine. The probability that the ball has a red
stripe is 1/9th the probability that the golf ball has no stripe. How many of the golf balls in the
dispensing machine have a red stripe?
a)108
b)120
c)150
d)251
e)320 "

Jay92 wrote:I ran into this on the gmatpill prep test

"There are 1,200 golf balls in a golf ball dispensing machine. The probability that the ball has a red
stripe is 1/9th the probability that the golf ball has no stripe. How many of the golf balls in the
dispensing machine have a red stripe?
a)108
b)120
c)150
d)251
e)320 "

This question is based on this assumption that there are only two types of golf balls in the dispensing machine, red stripe and no stripe. Hence, if p is the probability that the golf ball has no stripe, then p/9 is the probability that the ball has a red stripe. In that case, ratio in the two probabilities would also represent the ratio in their respective numbers present in the dispensing machine.

Using the ratio in the number of no stripe to number of red stripe as p: (p/9) = 9:1, we get the number of the golf balls in the dispensing machine having a red stripe

= [spoiler](1/10) × 1200 = 120.

Choose B[/spoiler]

The prompt should make it clear that each ball has either a red stripe or no stripe, as follows:

There are 1,200 golf balls in a golf ball dispensing machine. Each of the golf balls in the machine has either a red stripe or no stripe. If a ball is chosen at random, the probability that the ball has a red stripe is 1/9th the probability that the ball has no stripe. How many of the golf balls in the dispensing machine have a red stripe?

a)108
b)120
c)150
d)251
e)320

The probability that the ball has a red stripe is 1/9th the probability that the ball has no stripe.
In other words, the number of balls with no stripe is 9 times the number of balls with a red stripe.
Implication:
There are 9 balls with no stripe for every 1 ball with a red stripe.
Thus, of every 10 balls, 1 will have a red stripe, implying that the balls with a red stripe constitute 1/10 of the total number of balls:
(1/10)(1200) = 120.

The correct answer is B.