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.

Question

Luna Moreno

Mathematics

27 June, 00:27

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.

+2

Answers (1)

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Hadassah Park · 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