Conditional Probability Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
4 of 54 of 5 Items

Question
Use the table to answer the question.

Arrival Time
Transport Type On Time Late TOTAL
Car 230 20 250
Bicycle 70 130 200
TOTAL 300 150 450
Let event A
represent a late arrival and event B
represent transportation by car. What would the product of P(A)
and P(B)
need to equal to show that the events are independent? Express the answer as a decimal to the nearest hundredth.

(1 point)
Remaining Attempts : 2View previous attempt

Answer 1

To determine the product of \( P(A) \) and \( P(B) \) needed to show that the events are independent, we first need to calculate \( P(A) \) and \( P(B) \).

1. Finding \( P(A) \): Event A (Late Arrival) consists of 150 individuals who are late out of a total of 450. \[ P(A) = \frac{\text{Number of late arrivals}}{\text{Total individuals}} = \frac{150}{450} = \frac{1}{3} \approx 0.33 \]

2. Finding \( P(B) \): Event B (Transportation by Car) consists of 250 individuals who use a car out of a total of 450. \[ P(B) = \frac{\text{Number taking car}}{\text{Total individuals}} = \frac{250}{450} = \frac{5}{9} \approx 0.56 \]

3. Finding the product \( P(A) \times P(B) \): \[ P(A) \times P(B) = \left(\frac{1}{3}\right) \times \left(\frac{5}{9}\right) = \frac{5}{27} \approx 0.1852 \]

To express this as a decimal rounded to the nearest hundredth: \[ \frac{5}{27} \approx 0.19 \]

Thus, the product \( P(A) \times P(B) \) that would show the events are independent is: 0.19