2008 SAJC P2 Q8

A student has requested for a testimonial to apply for a job.

She estimates that there is an \(80\%\) chance of getting the job if she receives an excellent testimonial, a \(40\%\) chance if she receives a moderately good testimonial and a \(10\%\) chance if she receives a fair testimonial.

She further estimates that the probabilities that the testimonial will be excellent, moderate or fair are \(0.7, 0.2\) and \(0.1\) respectively.

1. Draw a tree diagram to illustrate the information and calculate the exact probability of the students getting the job.[2]
2. Given that she receives the job offer, what is the exact probability that she received an excellent testimonial?[2]
3. Given that she did not receive a moderate testimonial, what is the exact probability that she did not receive a job offer?[2]