Questions: There are two boxes containing only yellow and orange pens. Box A has 6 yellow pens and 9 orange pens. Box B has 13 yellow pens and 7 orange 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 an orange pen from Box B. Event 3: choosing a yellow pen from Box B. Event 4: choosing a yellow or orange pen from Box A. Least likely Most likely Event Event Event Event

There are two boxes containing only yellow and orange pens. Box A has 6 yellow pens and 9 orange pens. Box B has 13 yellow pens and 7 orange 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 an orange pen from Box B. Event 3: choosing a yellow pen from Box B. Event 4: choosing a yellow or orange pen from Box A.

Least likely Most likely

Event Event Event Event

Transcript text: There are two boxes containing only yellow and orange pens. Box $A$ has 6 yellow pens and 9 orange pens. Box $B$ has 13 yellow pens and 7 orange 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 an orange pen from Box B. Event 3: choosing a yellow pen from Box B. Event 4: choosing a yellow or orange pen from Box $A$. Least likely $\qquad$ Most likely Event $\square$ Event $\square$ Event $\square$ Event $\square$

Solution

Solution Steps

To determine the likelihood of each event, we need to calculate the probability of each event occurring. The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.

Event 1: choosing a yellow pen from Box A.
- Probability = Number of yellow pens in Box A / Total number of pens in Box A
Event 2: choosing an orange pen from Box B.
- Probability = Number of orange pens in Box B / Total number of pens in Box B
Event 3: choosing a yellow pen from Box B.
- Probability = Number of yellow pens in Box B / Total number of pens in Box B
Event 4: choosing a yellow or orange pen from Box A.
- Probability = Total number of pens in Box A / Total number of pens in Box A (since it's certain to pick a pen from Box A)

We will then compare these probabilities to list the events from least likely to most likely.

Step 1: Calculate the Total Number of Pens in Each Box

For Box $A$: \[ \text{Total pens in Box } A = 6 \text{ (yellow)} + 9 \text{ (orange)} = 15 \]

For Box $B$: \[ \text{Total pens in Box } B = 13 \text{ (yellow)} + 7 \text{ (orange)} = 20 \]

Step 2: Calculate the Probability of Each Event

Event 1: Choosing a yellow pen from Box $A$ \[ P(\text{Event 1}) = \frac{6}{15} = 0.4 \]

Event 2: Choosing an orange pen from Box $B$ \[ P(\text{Event 2}) = \frac{7}{20} = 0.35 \]

Event 3: Choosing a yellow pen from Box $B$ \[ P(\text{Event 3}) = \frac{13}{20} = 0.65 \]

Event 4: Choosing a yellow or orange pen from Box $A$ \[ P(\text{Event 4}) = \frac{15}{15} = 1.0 \]

Step 3: List Events from Least Likely to Most Likely

We compare the probabilities calculated in Step 2: \[ \begin{align_} P(\text{Event 2}) &= 0.35 \\ P(\text{Event 1}) &= 0.4 \\ P(\text{Event 3}) &= 0.65 \\ P(\text{Event 4}) &= 1.0 \end{align_} \]