Question

The following table is used for a number of questions below. The table above shows the responses of a survey of teenagers aged 14-18 when asked at what age they thought they would become financially independent.

Age of Financial Independence	Number of Responses
16-20	191
21-24	467
25-27	244
28 or older	42

1. What do the teens expect is the probability of being financially independent before age 25?
2. A recent Gallup poll found that only 14 percent of 24- to 34-year-olds are financially independent. Do teens have realistic expectations?

Answer 1

PART(1)

We know that probability is defined as the ratio of favourable outcome to the total outcome

In this case, total outcome = sum of all responses = 191+467+244+42 = 944

We have to find the probability of being financially independent before age 25, i.e. 16-20 and 21-24

So, favourable outcome = sum of responses for 16-20 and 21-24 = 191+467 = 658

This gives us

Probability = (favourable)/(total) = (658/944) = 0.6970

PART(2)

We know that probability is defined as the ratio of favourable outcome to the total outcome

In this case, total outcome = sum of all responses = 191+467+244+42 = 944

We have to find the probability of being financially independent between 24 to 34, i.e. 25-27 and above

So, favourable outcome = sum of responses for 25-27 and above = 244+42 = 286

This gives us

Probability = (favourable)/(total) = (286/944) = 0.3030

converting it to %, we get 0.3030*100 = 30.30%

So, it is clear that teens dont have realistic expectations because 30.30% is too high as compared to only 14%