Question

there are two boxes containing only purple and yellow pens. box a has 2 purple pens and 3 yellow pens. box b has 6 purple pens and 10 yellow pens. a pen is randomly chosen from each box. list these events from least likely to most likely. event 1: choosing a purple or yellow pen from box b. event 2: choosing a purple pen from box b. event 3: choosing a purple pen from box a. event 4: choosing a red pen from box a. least likely → most likely event , event , event , event

Explanation:

Step1: Calculate probabilities for each event

• For Event 1: In Box B, there are only purple and yellow pens. The probability of choosing a purple or yellow pen from Box B is $P_1 = 1$ (since all pens in Box B are either purple or yellow).
• For Event 2: In Box B, there are $6 + 10=16$ pens in total, and 6 are purple. So the probability of choosing a purple pen from Box B is $P_2=\frac{6}{16}=\frac{3}{8}$.
• For Event 3: In Box A, there are $2 + 3 = 5$ pens in total, and 2 are purple. So the probability of choosing a purple pen from Box A is $P_3=\frac{2}{5}$.
• For Event 4: In Box A, there are no red pens. So the probability of choosing a red pen from Box A is $P_4 = 0$.

Step2: Compare the probabilities

We have $P_4=0$, $P_2=\frac{3}{8}=0.375$, $P_3=\frac{2}{5} = 0.4$, $P_1 = 1$.
Since $0<0.375<0.4<1$, the order from least - likely to most - likely is Event 4, Event 2, Event 3, Event 1.

Answer:

Event 4, Event 2, Event 3, Event 1