A company is about to launch a new cell phone model. In the past, 40% of its cell phones have launched successfully. Before any cell phone is launched, the company conducts market research and receives a report predicting favorable or unfavorable sales. In the past, 70% of successful cell phones and 20% of unsuccessful cell phones received favorable reports.

What is the probability that the new cell phone will receive a favorable report, given that the cell phone launch is successful?

0.45

0.54

0.64

0.70

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Answered

Verified Answer :

nexlout nexlout · Answer 1 · 2016-09-04T10:12:43-04:00

The probability is 0.70

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virtuematane virtuematane · Answer 2 · 2019-03-07T04:52:51-05:00

Hence, the probability is:

0.70

Let x be the total cell phones.

Let A denote the event of cell phone will receive a favorable report.

B denote the event that the cell phone is launched successfully.

Now we have to find the probability:

P(A|B)

We know that P(A|B) is calculated as:

\(P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}\)

Now it is given that:

40% of its cell phones have launched successfully.

i.e. \(P(B)=0.4x\)

( Since,

\(\dfrac{40}{100}\times x=0.4x\)

Also,

In the past, 70% of successful cell phones and 20% of unsuccessful cell phones received favorable reports.

So, Number of successfully launched+favorable cell phones is successful are:

40% of 70% of the total cell phones.

i.e.

\(P(A\bigcap B)=\dfrac{70}{100}\times \dfrac{40}{100}\times x\)

Hence, the probability P(A|B) is:

\(\dfrac{\dfrac{40}{100}\times \dfrac{70}{100}\times x}{\dfrac{40}{100}\times x}\\\\\\\\=\dfrac{70}{100}=0.70\)[/tex]

Hence, the probability is:

0.70