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. Which of the following shows the correct calculation of P(A)⋅P(B)
?

(1 point)
Responses

150250+20250
Start Fraction 150 over 250 End Fraction plus Start Fraction 20 over 250 End Fraction

150250⋅20250
Start Fraction 150 over 250 End Fraction times Start Fraction 20 over 250 End Fraction

150450+250450
Start Fraction 150 over 450 End Fraction plus Start Fraction 250 over 450 End Fraction

150450⋅250450

Answer 1

To calculate \(P(A) \cdot P(B)\), we need to start by determining the probabilities of events \(A\) and \(B\).

1. **Calculating \(P(A)\)** (probability of a late arrival):
- There are 150 late arrivals out of a total of 450 arrivals.
- Therefore, \(P(A) = \frac{150}{450}\).

2. **Calculating \(P(B)\)** (probability of transportation by car):
- There are 250 total car arrivals out of a total of 450 arrivals.
- Therefore, \(P(B) = \frac{250}{450}\).

3. **Calculating \(P(A) \cdot P(B)\)**:
- Now, we multiply these probabilities:
\[
P(A) \cdot P(B) = \left(\frac{150}{450}\right) \cdot \left(\frac{250}{450}\right)
\]

This matches the option:
- \( \frac{150}{450} \cdot \frac{250}{450} \)

Thus, the correct response is:

**150450⋅250450**
\( \text{Start Fraction 150 over 450 End Fraction times Start Fraction 250 over 450 End Fraction} \)