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

The probability is 0.70

Answer 2

Hence, the probability is:

0.70

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)=(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,

`(40)/(100)* 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)=(70)/(100)* (40)/(100)* x`

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

`((40)/(100)* (70)/(100)* x)/((40)/(100)* x)\\\\\\\\=(70)/(100)=0.70`[/tex]

Hence, the probability is:

0.70