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

150450⋅250450
Start Fraction 150 over 450 End Fraction times Start Fraction 250 over 450 End Fraction

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

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

150450+250450

1 answer

To find the probabilities \( P(A) \) and \( P(B) \), we can use the values from the table provided.

  • \( P(A) \) represents the probability of a late arrival. The total number of late arrivals is 150, and the total number of arrivals (both on time and late) is 450. Thus,

\[ P(A) = \frac{150}{450} \]

  • \( P(B) \) represents the probability of transportation by car. The total number of arrivals by car is 250, and the total number of arrivals is 450. Therefore,

\[ P(B) = \frac{250}{450} \]

To calculate \( P(A) \cdot P(B) \), we multiply these two probabilities together:

\[ P(A) \cdot P(B) = \left(\frac{150}{450}\right) \cdot \left(\frac{250}{450}\right) \]

Thus, the correct response for \( P(A) \cdot P(B) \) is:

\[ \frac{150}{450} \cdot \frac{250}{450} \]

This aligns with the first response option:

\[ 150450 \cdot 250450 \text{ (Start Fraction 150 over 450 End Fraction times Start Fraction 250 over 450 End Fraction)} \]

So the correct answer is:

150450⋅250450