Question

There are two boxes containing only black and blue pens.Box A has 3 black pens and 5 blue pens.Box B has 5 black pens and 15 blue pens.A pen is randomly chosen from each box.List these events from least likely to most likely.Event 1: choosing a black or blue pen from Box A.Event 2: choosing a green pen from Box B.Event 3: choosing a black pen from Box B.Event 4: choosing a black pen from Box A.Least likelyMost likelyEvent | Event | EventEvent

Answer 1

Let's analyze each event

EVENT 1:

Since there are only black and blue pens in box A, it is a certanity that if you pick one at random, you'll choose a black or blue pen. This way,

$P(1)=1$

EVENT 2:

Since there are no green pens on box B, you cannot pick a green pen out. This way,

$P(2)=0$

EVENT 3:

Out of the 20 pens in box B, 5 are black. This way, the probability of choosing a black pen from box B is:

$\begin{gathered} P(3)=\frac{5}{15} \\ \\ \rightarrow P(3)=\frac{1}{3} \\ \\ \rightarrow P(3)=0.33 \end{gathered}$

EVENT 4:

Out of the 8 pens in box B, 3 are black. This way, the probability of choosing a black pen from box B is:

$\begin{gathered} P(4)=\frac{3}{8} \\ \\ \rightarrow P(4)=0.375 \end{gathered}$

This way, the list of events sorted from most likely to lest likely is

• Event 1

,

• Event 4

,

• Event 3

,

• Event 2