The local Automobile Association conducted a study of the incidences over a ten

Question

The local Automobile Association conducted a study of the incidences over a ten year period of children under the age of 5 years who were involved in motor vehicle accidents that resulted in at least one road fatality. The results for children who were not wearing seat belts at the time of the accident are shown in the following table: 6. Age Survivors Fatalities Total 265 227 492 204 191 367 207 574 606 571 Total 1629 1009 2638 190 194 477 b) Name the two random variables present in this table i) Develop a joint probability table that summarises the results of the study. ii) Construct the marginal probability distribution for the age variable. iv) Construct the marginal probability distribution for the other variable. v) Compute the probability that a child survives an accident given that the child is either 3 or 4 years old.

Explanation / Answer

i)

The first random variable is: Age

Teh second random variable is: Survivor

ii)

To develop the joint probability distribution we need to divide each value by 2638 (that is by the grand total). Following table shows the same, each value is rounded to 4 decimal places, :

iii)

The marginal distribution of age is shown by the row total. The marginal distribution of age is:

iv)

Following table shows the marginal distribution of survivors:

v)

From table we have:

P(age 3 or 4) = 0.1918 +0.2544 = 0.4462

P(survivors and age 3 or 4) = 0.1198 + 0.1808 = 0.3006

The required probability is

P(survivors | age 3 or 4) =  P(survivors and age 3 or 4) /  P(age 3 or 4) = 0.3006 / 0.4462 = 0.6737

Age Survivors Fatalities Total 0 0.1005 0.0861 0.1865 1 0.0773 0.0724 0.1497 2 0.1391 0.0785 0.2176 3 0.1198 0.072 0.1918 4 0.1808 0.0735 0.2544 Total 0.6175 0.3825 1

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.