Answer:
1st sentence is correct
4th sentence is correct
Explanation:
1st sentence :
Aunt Betsy somehow made it to her thirtieth birthday without changing a lightbulb; in fact, she didn't even know what one looked like.
This sentence is correct because here two similar sentences are connected by a semi colon.
2nd sentence :
Murphy's law essentially states this: Anything that can go wrong will go wrong.
This sentence is wrong because after semi colon the sentence is stared with a capital letter, it should be small letter.
3rd sentence :
She said; "Ouch!"
This sentence is wrong because comma should be used in place of semi colon.
4th sentence :
The team's problems centered in three positions: Jen Layland, first base; Debbie Meyer, catcher; and Maggie Smith, left field.
This sentence is correct because here three items or three terms are separated by a semi colon which are commas are used to show the relation of the three terms.
5th sentence :
For a bad day to happen, three elements are required; a stubbed toe, a bad attitude, and one car key locked in a car.
This sentence is wrong because the line "three elements are required" should be followed by a colon instead of a semi colon.
Thus, sentences 1 and 4 are correct.