Question

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

Answer 1

Answer:

Hence, the probability is:

0.70

Step-by-step explanation:

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

Answer 2

The probability is 0.70