Question

Box contains 4 bolts. two of them, labeled #1 and #2 are 5 mm in diameter, and two of them, labeled #3 and #4, are 7 mm in diameter. bolts are randomly selected until a 5 mm bolt is obtained. the outcomes are the sequences of the bolts that can be selected. so one outcome is 1, and another is 342. let x represent the number of bolts selected.

a.find the probability mass function of x.

Answer 1

This can be solved with a tree diagram, or a table, or a simple enumeration.
The following is the last method.
1
2
31
32
341
342
41
42
431
432
So there are 10 possible outcomes, out of which 2 have a single pick, 4 have 2 picks, and 4 have 3 picks.
The pmf of x is therefore
x p
1 1/5
2 2/5
3 2/5