Question

Please can you help with a question on probability from the Venn diagram given. ?

Answer 1

Choice (4)

Explanation:

It is given that the random person chosen for this survey does not take music. So the middle value (80, where the person likes both math and takes music) is out. Obviously, the 45 is also out because that is the part of the circle where the person only takes music.

What is left is the 22 (where the person only likes math), and the 38 which is in neither circle (meaning they neither like math nor takes music).

So, to find the probability, we are going to divide the number of people who like math (22), by the total people excluding those who play an instrument (22 + 38).

Now for some arithmetic: `22/(22+38)`

`=22/60`

`= 0.36` (pretend there is bar notation on the 6)

And for the sake of not having a repeating decimal for your answer, we will round it to hundredths:

`0.37`

Answer 2

`"P"("like Math" | "NOT take music") = 11/30`, or 36.67%.

Explanation:

This question involves conditional probability—the chance of an event `A` occurring, given that another event `B` has occurred.

Normally, when we consider just the probability of `A`, we look at the number of ways `A` can occur, and compare that to the number of ways anything can occur (i.e. anything from our sample space `S)`. Mathematically, this can be written as

`"P"(A) = ("size of "A)/("size of "S)`

and thought of as the fraction of `S` that is also in `A`.

When we have a conditional probability, such as the probability of `A` given that `B` has occurred, written as `"P"(A|B),` we must narrow our view. Since we are assuming `B` has occurred, it is not possible for anything outside of `B` to occur. Thus, `B` is like our new reduced sample space.

So, when we take the probability `"P"(A|B)`, we now look at the number of ways `A` can occur that are also in `B`, and compare that to the number of ways anything in `B` can occur. Mathematically, this can be written as

`"P"(A|B) = ("size of "(AnnB))/("size of "B)`

and thought of as the fraction of `B` that is also in `A`.

Solution:

In the given question, our sample space has a size of

`|S|=38+22+80+45`
`color(white)(|S|)=185`

Of these 185 students, 125 take music (80 + 45), while the other 60 do not (38 + 22).

Since we are interested in `"P"("like math" | "NOT take music"),` it is the 60 that do not take music that will be our "reduced sample space".

Now, of these 60 students that don't take music, how many also like math? From the Venn diagram, that's easy to see; it's 22. So, our conditional probability is:

`"P"("Math" | "NOT Music")`

`= ("size of "("Math" nn "NOT Music"))/("size of (NOT Music)")`

`= 22/60`,

which reduces to `11/30` or 36.67%.

Answer 3

answer 4

Explanation:

there are 38 who do not take music and do not like maths.
there are 22 who like maths but do not take music
so you have 38+22=60 people who do not take music
the probability of the chosen person liking maths is

`22/60=11/30=0.3dot6`

this rounds to 0.37