Someone could help me - Probability Exercise! Thank you!

Question

Over a long period of time in a large multinational corporation, 10% of all sales trainees are rated as outstanding, 75% are rated as execellent/good, 10% are rated as satisfactory, and 5% are considered unsatisfactory. Find the following probabilities for sample of 10 trainees selected at random.

A- Two are rated as outstanding

B- Two or more are rated as outstanding

C- Eight of the 10 are rated either outstanding or execellent/good

D- None of the trainees is rated as unsatisfactory

Answer 1

We first make a reasonable assumption from the line "large multinational corporation" that the population would be largely unchanged by pulling 10 employees out, as to not drastically change the supplicant odds.

A) Is asking for an exact outcome. We know 10% are outstanding, so we know the opposite is true, 90% are not outstanding.

(.1*.1*.9*.9*.9*.9*.9*.9*.9*.9*.9)=0.0043 or 0.43%

B) You know how much it takes for 2 outstanding exactly. so to have 2 OR MORE, you just need to take the same answer as previously and add some context

"at least 0.43%"

C) You can combine the percentages for outstanding and excellent/good, so 85%. Now just repeat the process from step A)

.85*.85*.85*.85*.85*.85*.85*.85*.15*.15=0.6%

D)likewise, combine the percentages for everything that is not unsatisfactory

(.95)^10= 59.9%