Statistics - It costs $50 to find out whether a spare part is required for repairing a failed device is...?

Question

It costs $50 to find out whether a spare part required for repairing a failed device is faulty or not. Installing a faulty spare part causes damage of $1000. Is it on average more profitable to use a spare part without checking if:

(i) 1% of all spare parts of that type are faulty?

(ii) 3% of all spare parts of that type are faulty?

(iii) 10% of all spare parts of type are faulty?

Please explain the answers. Thanks!

Answer 1

if the spare part is checked for fault, the expense will be as follows:

$50 - checking fee (THIS IS UR ONLY LOSS IF THE DEVICE IS FAULTY)

if the spare part is NOT checked for fault, the expense will be as follows:

since the chance of picking a faulty one is 50%,

(i) (1% / 50%) * $1000 = $20

-more profitable NOT TO CHECK since $20 < $50

(ii) (3% /50%) * $1000 = $60

-more profitable to CHECK since $60 > $50

(iii) (10% /50%) * $1000 = $200

-more profitable to CHECK since $200 > $50

=)

Answer 2

I'm not sure but check this out...

let's say you have 100 spare parts (both faulty and not)

with $50 but no repairs.... no checking costs but with repairs

(I)................4,950................. 1,000

(II)...............4,850................. 3,000

(III).............4,500..................  10,000

(I) answer: yes ($1,000 < $4,950)

(II) answer: yes ($3,000 < $4,850)

(III) answer: no ($10,000 > $4,500)

Answer 3

lets say there are 100 spare parts

i) it would mean 1 faulty spare part

so checking = 50* 100 = 5000

not checking = 1000 * 1 = 1000

1000 < 5000 more profitable to use without checking

ii) it would mean 3 faulty spare parts

50 * 100 = 5000

1000 * 3 = 3000

3000 < 5000 more profitable to use without checking

iii) it would mean 10 faulty spare parts

50 * 1000 = 5000

1000 * 10 = 10000

10000 > 5000 no not more profitable, in this case it is less profitable not checking

hope this helps