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]