question archive In a psychiatric practice a therapist said he randomly selected 5 patients and by coincidence she got the ones with the highest measurement of depression

In a psychiatric practice a therapist said he randomly selected 5 patients and by coincidence she got the ones with the highest measurement of depression

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In a psychiatric practice a therapist said he randomly selected 5 patients and by coincidence she got the ones with the highest measurement of depression. You don't believe him. What is the probability that out of 27 patients she would randomly get the 5 with the highest measures?(This one round off to 5 decimal places)

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0.18519

Step-by-step explanation

Suppose A is an event. P(A) or the probability that A will occur is given by

P(A)=total number of outcomesnumber of favorable outcomes to A?.

 

Let A = event that out of 27 patients a therapist would randomly get the 5 with the highest measures. By the theorem above, the number of favorable outcomes to A is 5 and the total number of outcomes is 27. So 

P(A)=275?

P(A)=0.1851851852

P(A)=0.18519