A car dealership sells Ford and Honda automobile. There are 6 black Fords and 5 silver Fords on the car lot. There are 4 black Hondas and 3 silver Hondas. a) Construct a 2-way table. The first row is Ford and the first column is black.b) Construct a Venn diagram for this situation.c)P(B and H) =?d) P(H / B)=?e) P(H or S)=?f) P(F)=?

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Mathematics

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A car dealership sells Ford and Honda automobile. There are 6 black Fords and 5 silver Fords on the car lot. There are 4 black Hondas and 3 silver Hondas. a) Construct a 2-way table. The first row is Ford and the first column is black.b) Construct a Venn diagram for this situation.c)P(B and H) =?d) P(H / B)=?e) P(H or S)=?f) P(F)=?

Answer :

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ANSWER and EXPLANATION

a) We want to create a 2-way table with the rows as the car types and the columns as the car color.

b) The venn diagram for the situation is:

c) To find the probability that the car is black and it is a Honda, divide the number of black hondas by the total number of cars:

[tex]\begin{gathered} P(BandH)=\frac{4}{18} \\ =\frac{2}{9} \end{gathered}[/tex]

d) To find the probability that the car is a Honda given that it is black, divide the number of Hondas that are black by the total number of black cars:

[tex]\begin{gathered} P(H|B)=\frac{P\mleft(HandB\mright)}{P(B)}=\frac{4}{10} \\ P(H|B)=\frac{2}{5} \end{gathered}[/tex]

e) To find the probability that the car is Honda or a silver color, find the probability of the car being black and silver, and subtract it from the sum of the probability of the car being black and the probability of the car being silver:

[tex]\begin{gathered} P(\text{HuS)}=P(H)+P(S)-P(\text{HnS)} \\ P(\text{HuS)}=\frac{7}{18}+\frac{8}{18}-\frac{3}{18} \\ P(\text{HuS)}=\frac{12}{18} \\ P(\text{HuS)}=\frac{2}{3} \end{gathered}[/tex]

f) To find the probability of the car being a Ford, divide the number of Fords by the total number of cars:

[tex]P(F)=\frac{11}{18}[/tex]