91Ó°ÊÓ

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.

The probability that a student does not have long hair means there is no student have long hair in a total number of students. The symbol of probability is given by,

$P\left(L^{\text{'}}\right)=1-P\left(L\right)$

The probability that a student is male or has short hair means there are either male students or short hair students. The symbol of probability is given by,

$P(M∪S)=P\left(M\right)+P\left(S\right)-P(Mâˆ\copyright S)$

The probability that a student is a female and has long hair means there are female students has long hair. The symbol of probability is given by

$P(Fâˆ\copyright L)=P\left(F\right).P\left(L\right)$

The probability that a student is male, given that the student has long hair means there are male students has long hair. The symbol of probability is given by

$P(Mâˆ\copyright L)=P\left(M\right).P\left(L\right)$

The probability that a student has long hair, given that the student is male means students who have long hair are male students. The symbol of probability is given by

$P(Lâˆ\copyright M)=P\left(L\right).P\left(M\right)$

Of all the female students, the probability that a student has short hair means the student has short hair out of all the female students. The symbol of probability is given by

$P\left(\overline{)F}S\right)=\frac{P(Fâˆ\copyright S)}{P\left(S\right)}$

Of all students with long hair, the probability that a student is female means the student is female among all long hair students. The symbol of probability is given by

$P\left(\overline{)L}F\right)=\frac{P(Lâˆ\copyright F)}{P\left(F\right)}$

The probability that a student is female or has long hair means that the students are either female or long hair students. The symbol of probability is given by

$P(Fâˆ\copyright L)=P\left(F\right).P\left(L\right)$

The probability that a randomly selected student is a male student with short hair means the male student with short hair. The symbol of probability is given by

$P(Mâˆ\copyright S)=P\left(M\right).P\left(S\right)$

The probability that a student is female. The symbol of probability is given by$P\left(F\right)$