Use the table to answer the question.

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 \( \text{Start Fraction 150 over 450 End Fraction times Start Fraction 250 over 450 End Fraction} \)