Question

Four emergency radios are available for rescue workers but one does not work properly.
Two randomly selected radios are taken on a rescue mission. Let X be the number that work properly between the two.
(a) Determine he probability distribution of f(x) of X.
(b) Determine the cumulative probability distribution F(x) of X.

Answer 1

I know that to obtain the probability distribution for f(x) of X, I need to
find the outcome of successes for working radios.(1) Since I can only choose two radios
the chances of me getting no working radio when X=0 is FS and SF (where S is the
sucess of getting a working radio and F is the failure of not getting a working
radio), or 1/2(4 is the denominator since there
are a total of four possible radios to choose from. The number of selections
is the numerator). (2) The possibility of me getting one successful radio out of two is also
1/2.

Answer 2

I'm still trying to figure out the second one but I'm pretty sure that the irst part is correct.

Answer 3

I think for part b I have to take X as the numerator and the denominator as 2 (being the random selection) so for X=0, the distribution would be 0, for 1, 1/2 and for 2, 1. This is the answer my book gets (0, .5, and 1.0)