Answer to Question #235283 in Statistics and Probability for Lungu Michael

Question

Hospital records show that of patients suffering from a certain disease, 25% die

of it.

(i) What is the probability that of 6 randomly selected patients, 4 will recover?

[3 marks]

(ii) What is the most probable number of recoveries out of 6 randomly selected

patients?

Answer 1

The number of recovered patient follow a binomial distribution with n=6, p=1-0.25=0.75.

(i) $P(X=4)=C_6^40.75^40.25^2=0.2966.$

(ii) $E(X)=np=6*0.75=4.5.$