Question

Find each probability of the events and place them in order

Answer 1

Considering Box A,

Total number of pens = 3 + 5 = 8 pens

Probability of picking a purple (P) and black (B) pen is given below as,

$\begin{gathered} P(P)=\frac{3}{8} \\ P(B)=\frac{5}{8} \end{gathered}$

Considering Box B,

Total number of pens = 15 + 5 = 20 pens

Probability of picking a purple and black pen is given below as,

$\begin{gathered} P(P)=\frac{15}{20} \\ P(B)=\frac{5}{20} \end{gathered}$

For event 1, probability of choosing a red (R) pen from Box B is zero because there is no red pen in the Box.

Event 1 P(R) = 0

For event 2, probability of choosing a purple or black pen from Box A is,

$P(P\text{ or B)=}\frac{3}{8}+\frac{5}{8}=\frac{3+5}{8}=\frac{8}{8}=1$

Event 2 P(P or B) = 1

For event 3, probability of choosing a purple pen from Box A is,

$P(P)=\frac{3}{8}$

Event 3 (P) = 3/8

For event 4, probability of choosing a black pen from Box B is given below as,

$P(B)=\frac{5}{20}=\frac{1}{4}$

Event 4 P(B) = 1/4

Arranging each events from the least likely to the most likely is in the order below

$\text{Event 1, Event 4, Event 3, Event 2}$

Answer deduced above.