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Q. 1) A box contains four bolts. Two of them, labeled#1and #2, are 5 mm in diame

ID: 3044720 • Letter: Q

Question

Q. 1) A box contains four bolts. Two of them, labeled#1and #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 bolts that can be selected. So one outcome is 1, and another is 342 a. List all the possible outcomes b. Let A be the event that only one bolt is selected. List the outcomes in A c. Let B be the event that three bolts are selected. List the outcomes in B d. Let C be the event that bolt #2 is selected. List the outcomes in C. e. Let D be the event that bolt #4 is not selected. List the outcomes in D f. Let E be the event that bolt #1 is selected. Are A and E mutually exclusive? How about B and E, C and E, D and E?

Explanation / Answer

Label #1 and # 2 - 5mm bolts

Label # 3 and # 4 - 7 mm bolts.

Bolts are selected until 5 mm bolt is selected.

a. Possible outcomes

when the first selected bolt is 5 mm - 2 Outcomes - 1 , 2

When the first bolt selected is 7mm and select bolt is 5 mm - 4 outcomes - 31, 32, 41, 42

when the first two bolts selected are 7 mm and the third bolt is the 5mm - 4 outcomes - 341, 342, 431, 432

So the possible outcomes are : 1,2,31,32,41,42,341,342,431,432

b. Let A be the event that only one bolt is selected - when the first selected bolt is 5 mm - 2 Outcomes - 1 , 2

Outcomes in A : 1,2

c. Let B be the event that three bolts are selected . - when the first two bolts selected are 7 mm and the third bolt is the 5mm - 4 outcomes - 341, 342, 431, 432

Outcomes in B : 341, 342, 431, 432

d. Let C be the event that #2 is slected.

- When # 2 - 5mm bolt selected first time - Outcome 2 ;

- When #3 - 7mm bolt is selected first time and #2 - 5mm bolt selected second time -outcome 32

- When #4 - 7mm bolt is selected first time and #2 - 5mm bolt selected second time -outcome 42

- When #3 and #4 - 7mm bolts selected for the 1st and 2nd time resepectively and #2 - 5mm bolt selected thrid time - outcome - 342

-When #4 and #3 - 7mm bolts selected for the 1st and 2nd time resepctively and  #2 - 5mm bolt selected thrid time - outcome - 432

Outcomes in C - 2, 32, 42, 342,432