Probability question ... help

Hi,
just wondering if someone could please help me with this probability question?

Four colored balls in a basket: gray, green, blue, and red
A person reaches into the basket without looking, and picks out each of the four balls one at a time. What is the probability of selecting: gray, green, blue, red … in that order, without replacement?

I gave it a try but would like to have the correct answer, along with the proper formula which also displays the condition that the balls need to be selected in order



P(A)
P(gray, green, blue, red)
1/4 x 1/3 x 1/2 x 1/1 = 1/24 = 4.16%

but in order to address permutation ... you could use a factorial: 4! = 24

not sure what to do next?

thanks for any help
david

JeffM said:

I think your problem is that you lack confidence.

ONE way to address this problem is to ask, as you did, how many ways are there to pick the balls in different orders, which is 4!, or 24. So the probability of any one way is 1/24. Done.

OR you can think in terms of conditional probability, as you did, and up with

\(\displaystyle \dfrac{1}{4} * \dfrac{1}{3} * \dfrac{1}{2} * \dfrac{1}{1} = \dfrac{1}{24}.\) Done.

You found two different ways to get the SAME answer. This should reassure you, not disturb you.

Click to expand...

Thanks for taking the time to answer, much appreciated ... for some reason I was hoping for something more complex