## yashar806 2 years ago Probability

1. yashar806

There are four patients on the neo-natal ward of a local hospital who are monitored by two staff members. Suppose the probability (at any one time) of a patient requiring attention by a sta member is 0.3. Assuming the patients behave independently, what is the probability at any one time that there will not be suffccient staff to attend to all patients who need them?

2. satellite73

no time interval is mentioned, so my only guess is to solve having 3 or 4 patients need help

3. yashar806

(A) 0.0756 (B) 0.1104 (C) 0.0837 (D) 0.0463 (E) 0.2646

4. satellite73

you are told that these are independent events, which is a set up for using the binomial probability

5. yashar806

it is a multiple choice question

6. satellite73

the probability that three will need it is \[P(x=3)=\binom{4}{3}(.3)^3(.7)\] and the probability that all four will need it is \[P(x=4)=.3^4\] add these up

7. satellite73

of course \(\binom{4}{3}=4\)

8. yashar806

you mean solve for that equation

9. satellite73
10. yashar806

ok, i got it thanks so much

11. satellite73

it is not an equation, it is a computation requiring a calculator for sure

12. satellite73

yw

13. yashar806

sorry, where did you get that 3 ?

14. satellite73

you mean when i wrote \(P(X=3)\) ?

15. yashar806

is int 2?

16. yashar806

yes

17. satellite73

i was calculating the probability that 3 patients needed help

18. yashar806

how.?

19. yashar806

why three of them needed help/?

20. satellite73

\[P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\]

21. satellite73

there are two staff members and 4 patients if there are not enough staff members that means either 3 patients need help or 4 patients need help

22. yashar806

oh, now I totally got it

23. satellite73

the question asked "what is the probability at any one time that there will not be suffccient staff to attend to all patients who need them?"

24. yashar806

ok thx

25. satellite73

yw