Homework help statistic

Question

Suppose there are 10 females and 15 males. Select 3 people.

(a) How many ways can we select 3 people?

(b) How many ways can we select 3 females?

(c) Find 𝑃(3 𝑓𝑒𝑚𝑎𝑙𝑒𝑠)

(d) How many ways can we select 2 females? Keep in mind, we must select 3 people.

(e) Find 𝑃(2𝐹 𝑎𝑛𝑑 1𝑀)

(f)𝑃(1𝐹 𝑎𝑛𝑑 2𝑀)

(g) 𝑃(0𝐹 𝑎𝑛𝑑 3𝑀)

Answer 1

n = total number of people (10 females and 15 males) = 25

a) C(25,3) = 25! / (3! 22!) = 2300 ways to choose 3 people

b) C(15,3) = 15! / (3! 12!) = 455 ways to choose 3 females

c) P(3 females) = C(15,3) / C(25,3) = 455/2300 = 0.1978

The probability of selecting 3 females is 0.1978.

d) C(15,2)*C(10,1) = 105*10 = 1050 ways to choose 2 females and 1 male

e) P(2 females and 1 male) = [C(15,2)*C(10,1)] / C(25,3) = 1050/2300 = 0.4565

The probability of selecting 2 females and 1 male is 0.4565.

f) P(1 female and 2 males) = [C(15,1)*C(10,2)] / C(25,3) = 675/2300 = 0.2935

The probability of selecting 1 female and 2 males is 0.2935.

g) P(0 females and 3 males) = [C(15,0)*C(10,3)] / C(25,3) = 120/2300 = 0.0522

The probability of selecting no females and 3 males is 0.0522.