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There are 10 patients on the neonatal ward of a local hospital who are monitored by...

There are 10 patients on the neonatal ward of a local hospital who are monitored by 2 staff members. If the probability (at any one time) of a patient requiring emergency attention by a staff member is .3, assuming the patients to be behave independently, what is the probability at any one time that there will not be sufficient staff to attend all emergencies?

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Answer #1

Solution

This is a binomial distribution with parameters
n = 10, p = 0.3 and q = 0.7

the formula for k patients simultaneously needing attention will be
P[k] = 10Ck*(0.3)k*(0.7)(10-k)

we want to find P(k[>2) = 1 - (P[0] + P[1] +P[2])

= 1 - [ (0.7)10 + 10C1*(0.3)(0.7)9 + 10C2(0.3)2(0.7)8 ]

= 0.6172

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