A smart phone company is facing a problem. Ten out of every 75 phones they sell are having issue with the touchscreen, but the company doesn't know which ones have this issue until a buyer complains. Suppose the company makes a $300 profit on the sale of each working phone, but suffers a loss of $400 for every faulty phone because they have to repair the unit.

Check whether the company can expect a profit in the long term for their smart phones.

Question

Mathematics

Sariah Nichols

27 September, 13:14

A smart phone company is facing a problem. Ten out of every 75 phones they sell are having issue with the touchscreen, but the company doesn't know which ones have this issue until a buyer complains. Suppose the company makes a $300 profit on the sale of each working phone, but suffers a loss of $400 for every faulty phone because they have to repair the unit.

Check whether the company can expect a profit in the long term for their smart phones.

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Russell Schwartz · Answer 1

Per phone, there is an expected profit of $206.69. This means that the company can expect a profit in the long term for their smart phones.

Step-by-step explanation:

Ten out of every 75 phones they sell are having issue with the touchscreen

10/75 = 0.1333

0.1333 of the phones have issues with the touch.

The other 1-0.1333 = 0.8667 do not have issues with the touch.

Check whether the company can expect a profit in the long term for their smart phones.

0.1333 of the time, loss of $400.

0.8667 of the time, profit of $300.

So the expected earnings per phone will be:

E = - 0.1333*400 + 0.8667*300 = $206.69

Per phone, there is an expected profit of $206.69. This means that the company can expect a profit in the long term for their smart phones.