Question

there are two boxes containing only yellow and purple pens. box a has 15 yellow pens and 5 purple pens. box b has 3 yellow pens and 12 purple pens. a pen is randomly chosen from each box. list these events from least likely to most likely. event 1: choosing a yellow pen from box a. event 2: choosing a purple pen from box b. event 3: choosing a black pen from box b. event 4: choosing a yellow or purple pen from box a. least likely → most likely event ☐ , event ☐ , event ☐ , event ☐

Explanation:

Step1: Calculate probability of Event 1

Box A has 15 yellow + 5 purple = 20 pens. Probability of yellow from A: $\frac{15}{20} = 0.75$.

Step2: Calculate probability of Event 2

Box B has 3 yellow + 12 purple = 15 pens. Probability of purple from B: $\frac{12}{15} = 0.8$.

Step3: Calculate probability of Event 3

Box B has no black pens. Probability of black from B: $0$.

Step4: Calculate probability of Event 4

Box A has only yellow or purple. Probability: $\frac{20}{20} = 1$.

Step5: Order probabilities

0 (Event 3) < 0.75 (Event 1) < 0.8 (Event 2) < 1 (Event 4).

Answer:

Event 3, Event 1, Event 2, Event 4