A bit confused Any assistnace or how I should start this is

A bit confused. Any assistnace or how I should start this is appreciated.

A botanist is testing a process that has a 0.78 probability of success until she obtains two successes in a row or she runs the process 5 times. Let X be the number of times she runs the process. List all possible for this experiments. List all possible values of X. Make a table to show the pmf for X.

Solution

0.78 is the success probability untill two success or 5 times is taken.

a) posible outcomes of the experiment will be : either success with probability 0.78 or failure with probability 1-0.78 = 0.22

b) possible values of x can be = 1,2,3,4,5 (as above 5 no use it will end up in failure)

c) pmf :

X PROBABILITY

1 0.78 WINNING

2 0.78 WINNING

3 0.22 FAILURE

4 0.22 FAILURE

5 0.22 FAILURE ( BECOZ IT HAS GOT TWO SUCCESS IN FIRST TWO )