Question

1. carol records some cars that pass by her house.

a) complete the table above.
one of the cars is chosen. calculate the probability of choosing
b) a red car.
c) a grey volvo.
a ford is chosen. calculate the probability of
d) it being blue.

Explanation:

Step1: Complete the table

• Grey Volvo: \(31-(9 + 14)=8\)
• Red Ford: \(23-(4 + 11)=8\)
• Total Renault: \(60-(12 + 25)=23\)
• Blue Volvo: \(12-(8 + 4)=0\)
• Blue Renault: \(23-(9 + 11)=3\)
• Blue Ford: \(25-(14 + 8)=3\)
• Blue total: \(0 + 3+3 = 6\)

Step2: Probability of a red car

The formula for probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
Number of red cars \(n = 23\), total number of cars \(N=60\).
\(P(\text{red})=\frac{23}{60}\)

Step3: Probability of a grey Volvo

Number of grey Volvos \(n = 8\), total number of cars \(N = 60\).
\(P(\text{grey Volvo})=\frac{8}{60}=\frac{2}{15}\)

Step4: Probability of a blue Ford given a Ford is chosen

Number of blue Fords \(n = 3\), total number of Fords \(N=25\).
\(P(\text{blue}|\text{Ford})=\frac{3}{25}\)

Answer:

a) Grey Volvo: \(8\); Red Ford: \(8\); Total Renault: \(23\); Blue Volvo: \(0\); Blue Renault: \(3\); Blue Ford: \(3\); Blue total: \(6\)
b) \(\frac{23}{60}\)
c) \(\frac{2}{15}\)
d) \(\frac{3}{25}\)