Question

Suppose in a particular college ,60 % of the Student population is Female.

(a) Calculate the Probability that a class of 10 students will have exactly four females.

(b) Calculate the Probability that a class of 10 students will contain five,six or seven females.

(c) Calculate the Probability that at least five students in a class of 10 will be female

Answer 1

Let p denote the probability of females p=0.6

$q=1-p=0.4$

(a) Probability that a class of 10 students will have exactly four females.

$=^{10}C_4p^4q^6$

$= ^{10}C_4(0.6)^4(0.4)^6$

$=0.1114$

(b) Probability that a class of 10 students will contain five,six or seven females.

$=^{10}C_5p^5q^5+^{10}C_6p^6q^4+^{10}C_7p^7q^3$

$=^{10}C_5(0.6)^5(0.4)^5+^{10}C_6(0.6)^6(0.4)^4+^{10}C_7(0.6)^7(0.4)^3\\=0.2006+0.2508+0.2149\\=0.6663$

(c) Probability that at least five students in a class of 10 will be female

$=^{10}C_5p^5q^5+^{10}C_6p^6q^4+^{10}C_7p^7q^3+^{10}C_8p^8q^2+^{10}C_9p^9q+^{10}C_{10}p^{10}$

$=^{10}C_5(0.6)^5(0.4)^5+^{10}C_6(0.6)^6(0.4)^4+^{10}C_7(0.6)^7(0.4)^3+^{10}C_8(0.6)^8(0.4)^2+^{10}C_9(0.6)^9(0.4)+^{10}C_{10}(0.6)^{10}\\=0.2006+0.2508+0.2149+0.1209+0.0403+0.00604\\=0.83354$