There are male and female students. Some students have long hair and some students have short hair.

Question

...Write the symbols for the probabilities of the following events.

 

• Let F be the event that a student is female

• Let M be the event that a student is male

• Let S be the event that a student has short hair

• Let L be the event that a student has long hair

 

 

a.The probability that a student does not have long hair.

b. The probability that a student is male or has short hair.

c. The probability that a student is a female and has long hair.

d. The probability that a student is male, given that the student has long hair.

e. The probability that a student has long hair, given that the student is male.

f. Of all the female students, the probability that a student has short hair.

g. Of all students with long hair, the probability that a student is female.

h. The probability that a student is female or has long hair.

i. The probability that a randomly selected student is a male student with short hair.

j. The probability that a student is female.

Answer 1

1. Pr(F) = nF/(nF+nM)

2. PrM = nM/(nF+nM) = 1-PrF

3. PrL = nL/(nL+nS)=1-PrS

4. PrS= nS/(nS+nL) = 1-PrL

assuming everyone is F or M, and no trans, no nonbinary, no inbetweens

assuming everyone is L or S, and no in-between haired

helps to draw a Venn diagram, with 2 overlapping circles

a. Pr(~L) = PrS = nS/(nS+nL) = 1-PrL

b. Pr(MvS) = PrM+PrS -Pr(M^S) =Union minus Intersection = MUS-intersection (use an Upside down U symbol) of M and S

c. Pr(F^L) = (PrF+PrL) - 1

d. Pr(M/L) use Bayes Theorem for the conditional probabilities, PrMPr(L/M)= PrLPr(M/L) then P(M/L) = PrMPr(L/M)/PrL

e. Pr(L/M) = same as above, after switching L and M

f. Pr(S/F) =same as above but use S or L and F or M in d.

g. Pr(L/F) = same as above but replace S by L

h. Pr(FvL) = PrF + PrL - Pr(F^L)

i. Pr(M^S) = PrM +PrS -1

j. PrF = 1- PrM