A store has two gumball machines, which are stocked with maroon and gold gumballs. One machine has 100 maroon gumballs and 150 gold gumballs. The other has 150 maroon gumballs and 200 gold gumballs. THe owner has found out that customers are buying gu m from the first machine 40% of the time and from the second machine 60% of the time.
a. What is the probability that a customer gets a maroon gumball?
b. If a customer gets a gold gumball, what is the probability that it came from the first machine?
What I got...
a. P(maroon) = (250 maroon gumballs / 600 total gumballs) = 5/12
I'm not too sure because of the 40% and 60%. Does that play a factor to the problem?
b. We learned about this formula:
I suppose I would need to know if part a is right before I can continue.
Hello, toop!
You can't "dump them together" like that . . .A store has two gumball machines, which are stocked with maroon and gold gumballs.
Machine A has 100 maroon gumballs and 150 gold gumballs.
Machine B has 150 maroon gumballs and 200 gold gumballs.
The owner has learned that customers are buying from Machine A 40% of the time
and from Machine B 60% of the time.
(a) What is the probability that a customer gets a maroon gumball?
. . Hence: .
. . Hence: .
Therefore: .
I would use Bayes' Theorem: .(b) If a customer gets a gold gumball, what is the probability that it came from Machine A?
We have: . .[1]
. . We know: .
. . And: .
Substitute into [1]: .