Celeste wishes to hire a taxicab from a company which has a large number of taxicabs.

The taxicabs are randomly assigned by the company.

     The probability that a taxicab is yellow is 0.4.

     The probability that a taxicab is a Fiat is 0.3.

     The probability that a taxicab is yellow or a Fiat is 0.6.

 Find the probability that the taxicab hired by Celeste is not a yellow Fiat.

recognize need for intersection of Y and F     (R1)

eg     \({\text{P}}(Y \cap F){\text{, }}0.3 \times 0.4\)

valid approach to find \({\text{P}}(Y \cap F)\)     (M1)

eg     \({\text{P}}(Y) + {\text{P}}(F) - {\text{P}}(Y \cup F)\), Venn diagram

correct working (may be seen in Venn diagram)     (A1)

eg     \(0.4 + 0.3 - 0.6\)

\({\text{P}}(Y \cap F) = 0.1\)     A1

recognize need for complement of \(Y \cap F\)     (M1)

eg     \(1 - {\text{P}}(Y \cap F){\text{, }}1 - 0.1\)

\({\text{P}}\left( {(Y \cap F)'} \right) = 0.9\)     A1     N3

[6 marks]