Question

Every afternoon, Elizabeth enjoys a cup of hot tea in one of her many teacups. Once, Elizabeth counted all the teacups in her collection, noting their colors and size. Small Medium Green 4 2 Yellow 3 3 What is the probability that a randomly selected cup is yellow or medium? Simplify any fractions.

Answer 1

We have to calculate the probability that a randomly selected cup is yellow OR medium.

We can calculate the probability of an event as the quotient between the frequency of the event and the total frequency.

In this case, the event is the cup being yellow or medium.

As we have two groups, we calculate the union of this groups as:

`\begin{gathered} F(Y\cup M)=F(Y)+F(M)-F(Y\cap M) \\ F(Y\cup M)=(3+3)+(2+3)-3 \\ F(Y\cup M)=6+5-3 \\ F(Y\cup M)=8 \end{gathered}`

We substract the intersection of the two groups so as not to add the intersection twice.

NOTE: F in this case represents the absolute frequency of the class.

The total frequency is the sum of all the cups:

`N=4+2+3+3=12`

Then, we can calculate the probability of selecting a yellow or medium cup as:

`p(\text{Y or M})=(F(Y\cup M))/(N)=(8)/(12)=(2)/(3)`

Answer: the probability of selecting a yellow or medium cup is P = 2/3.