# A group of yr11 students aked to choose subjects for yr12. 135 chose mathematics subject (m) 84 chose language (L), 55 chose both. Find probability Pr(M) Pr(L) Pr(MnL)you can use a venn diagram and...

A group of yr11 students aked to choose subjects for yr12. 135 chose mathematics subject (m) 84 chose language (L), 55 chose both.

Find probability

Pr(M)

Pr(L)

Pr(MnL)

you can use a venn diagram and also find pr(MuL)

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### 1 Answer

You don't mention how many people chose neither. So I am going to say that there n students who chose neither.

There are 135 students who chose math, and 55 who chose both, so there are 135-55 = 80 students who chose math but didn't choose language

There are 84 students who chose language, and 55 who chose both, so there are 84-55=29 students who chose language but not math.

So we have:

n students who chose neither

80 students who chose math and not language

29 students who chose language and not math

55 students who chose both language and math

----

164 students taking math or language (or both)

164+n total students

`Pr(M)` = math students / total students = `135/(164+n)`

`Pr(L)` = language students / total students = `84/(164+n)`

`Pr(M uu L)` = (students taking math or language or both) / total students = `164/(164+n)`

`Pr(M nn L)` = (students taking neither) / total students = `n/(164+n)`

So for example, if there were 10 students taking neither:

`Pr(M) = 135/174`

`Pr(L) = 84/174`

`Pr(M uu L) = 164/174`

`Pr(M nn L) = 10/174`

Or, if there were 0 students taking neither (which might be your scenario, but I didn't want to assume)

`Pr(M) = 135/164`

`Pr(L) = 84/164`

`Pr(M uu L) = 164/164=1`

`Pr(M nn L) = 0/164=0`