I have a problem with this question about a probability distribution table. I'm getting the wrong answer but I cannot figure why this is so. Here's the question:
A small farm has 5 ducks and 2 geese. Four of these birds are to be chosen at random. The random variable X represents the number of geese chosen.
(i) Draw up the probability distribution of X.
I know that it will look like this:
x 0 1 2
I'm getting the values 0.26 for 0, 0.417 for 1 and 0.25 for 2. All of these are wrong, according to the book. Here's what I did:
for P(X=0): 4C0(2/7)^0(5/7)^4 = 625/2401 or 0.2603
for P(X=1): 4C1(2/7)^1(5/7)^3 = 1000/2401 or 0.4165
for P(X=2): 4C2(2/7)^2(5/7)^2 = 600/2401 or 0.2498
If I'm doing something wrong, I'd really like to know what it is because I've checked the above workings several times and keep getting the values above.
Any help would be appreciated.